Confused and have questions? Head over to Chegg and use code “CS5OFFBTS18” to get $5 off your first month of Chegg Study, so you can understand any concept by asking a subject expert and getting an in-depth explanation online 24/7. Plus get 30 minutes of one-on-one help with Chegg Tutors free!

Angles and Right Triangles

Angle Basics
Animation:  Types of Angles
Animation:  Measuring Angles with a Protractor
Angle Relationships and Types of Triangles
The Measure of the Interior Angles of Overlapping Triangles (No Algebra)
The Measure of the Interior Angles of Overlapping Triangles (Algebra)
Identify Complementary, Supplementary and Vertical Angles
Find the Measure of Complementary, Supplementary and Vertical Angles
Determine the Complement and Supplement of a Given Angle
Similar Triangles and Polygons
Ex:  Simplifying Square Roots (perfect squares)
Ex:  Simplifying Square Roots (not perfect squares)
Ex:  Estimating Square Roots with a Calculator
The Pythagorean Theorem
The Pythagorean Theorem and the Converse of the Pythagorean Theorem
Animation:  The Sum of the Interior Angles of a Triangle
Working with Degrees, Minutes, and Seconds
Convert an Angle in Degrees and Minutes to Degrees Only and Radians
Convert an Angle in Degrees, Minutes, and Seconds  to Degrees Only and Radians
Using the TI-84 to Convert Degrees, Minutes, and Seconds to Degrees and Radians
Using the TI-84 to Convert Degrees to Degree, Minutes, and Seconds and to Radians
Angles in Standard Position
Animation:  Angles in Standard Position
Ex:  Determine Angles of Rotation
Find The Measure of Angles in Standard Position (Degrees -360 to 360)
Determine the Measure of Reference Angles (No Algebra)
Determine the Measure of Reference Angles (Algebra)
Determine Reference Angles of Angles Between 0 and 360 Degrees
Determine Reference Angles of Angles Between -360 and 0 Degrees
Determine Reference Angles of Angles Given in Radians (Pos and Neg)
Determine Uncommon Reference Angles of Angles Given in Radians
Ex:  Determine if Two Angles Are Coterminal
Ex:  Determine a Coterminal Angle Between 0 and 360 Degrees
Ex:  Determine Positive and Negative Coterminal Angles

Trigonometric Functions Using Right Triangles

Congruent and Similar Triangles
Introduction to Trigonometric Functions Using Triangles
Find Trig Function Values Using a Right Triangle - Length of Hypotenuse Missing
Ex:  Determine What Trig Function Related Specific Sides of a Right Triangle
Ex:  Determine Trig Function Value Given a Right Triangle
Ex:  Determine the Length of a Side of a Right Triangle Using a Trig Equation
30-60-90 and 45-45-90 Reference Triangles
Solving 30-60-90 and 45-45-90 Right Triangles
Ex: Solve a 30-60-90 Triangle
Ex: Solve a 45-45-90 Right Triangle
Ex:  Determine the Perimeter of an Equilateral Triangle Given the Height

Trigonometric Function Values Using Angles in Standard Position

Introduction to Trigonometric Function Using Angles in Standard Position
Properties of Trig Functions:  Domain, Range, and Sign in each Quadrant
Trig Identities:  Reciprocal, Quotient, Pythagorean
Determine Trigonometric Function Values on the Calculator
Determine the Reference Angle of an Angle Given in Radians (4pi/3 and 11pi/4)
Determine the Reference Angle of an Angle Given in Radians (11pi/6 and 4)
Find Angles Given the Reference Angle and Trig Function Value Sign (45)
Find Angles Given the Reference Angle and Trig Function Value Sign (68)
Determine Trigonometric Function Values using Reference Angles and Reference Triangles.
Ex:  Determine the Reference Angle for a Given Angle
Ex:  Determine the Quadrant of the Terminal Side of An Angle Given Trig Function Signs
Ex:  Determine the Area of a Triangle Using the Sine Function
Find Sine, Cosine, and Tangent Values for 120 Degrees (Reference Triangle and Unit Circle)
Find Sine, Cosine, and Tangent Values for 225 Degrees (Reference Triangle and Unit Circle)
Find 6 Trig Function Values of 210 Degrees (Reference Triangle and Unit Circle)
Find 6 Trig Function Values of 315 Degrees (Reference Triangle and Unit Circle)
Find Trigonometric Function Values for 0 Degrees or 0 Radians
Ex:  Determine Trig Function Values Using Reference Triangles
Sine and Cosine Values in Radians Using Reference Triangles - Multiplies of pi/6 and pi/3
Sine and Cosine Values in Radians Using Reference Triangles - Multiplies of pi/4
Ex:  Sine and Cosine Values Using Reference Triangles - Degrees
Ex:  Find Six Trig Function Values Using Reference Triangles - Negative Degrees
Ex:  Find Six Trig Function Values Using Reference Triangles - Mult. of pi/6
Ex:  Find Six Trig Function Values Using Reference Triangles - Mult. of pi/4

The Unit Circle

Find Points on the Unit Circle Given Angles in Radians
Find Angles Given Points on the Unit Circle [0,2pi)
Find Points on the Unit Circle Given Angles in Degrees (Pos and Neg)
Determine Trigonometric Function Values using the Unit Circle
Ex:  Sine and Cosine Values Using the Unit Circle - Multiples of 30 degrees
Ex:  Sine and Cosine Values Using the Unit Circle - Multiples of 30, 45 degrees
Ex:  Sine and Cosine Values Using the Unit Circle - Multiples of pi/6 radians
Ex:  Sine and Cosine Values Using the Unit Circle - Multiples of pi/4 radians
Ex:  Determining Basic Trig Function Values Using The Unit Circle
Ex:  Determining Trig Function Values Using The Unit Circle
Ex: Find a Point on the Unit Circle Given One Coordinate

 Determining Trigonometric Function Values and Angles

Ex:  Determine Trig Function Values Given a Point on the Terminal Side of an Angle
Ex:  Determine Trig Function Values from Given Information
Ex:  Angles that Have the Same Sine and Cosine Function Values
Ex:  Find the Point on a Circle Given an Angle and the Radius
Ex: Find Trig Function Values Given the Cosine Value and Quadrant
Ex: Find Trig Function Values Given the Sine Value and Quadrant - Irrational
Ex: Find Trig Function Values Given the Tangent Value and Quadrant
Given tan(A)=-5/7 and sin(A)>0, Find sin(A) and cos(A)
Given sin(A)=2/5 and Quadrant of A, Find 5 Trig Function Values
Find Trig Function Values Given Sine and Quadrant
Find Sine and Cosine Given Tangent Value and Sign of Sine Value
Find 5 Trig Function Values Given Tangent Value and the Sign of Sine
Ex: Find Half Angle Trigonometric Function Values Given Cosecant of an Angle
Ex:  Determine Angles that have the same Trig Function Value Using the Unit Circle
Ex:  Determine Angles with the Same Trig Function Value
Ex:  Angles that Have the Same Sine and Cosine Function Values
Ex:  Find the Point on a Circle Given an Angle and the Radius

Solving Right Triangles

Intro to Inverse Trig Functions to solve right triangles
Ex:  Determine the Measure of an Angle of a Right Triangle
Properties of Trig Functions:  Domain, Range, and Sign in each Quadrant
Solving Right Triangles: Part 1:  The Basics
Use Tangent to Determine The Length of an Adjacent Side of a Right Triangle
Use Cosine to Determine The Length of a Hypotenuse of a Right Triangle
Use Sine to Determine The Length of a Hypotenuse of a Right Triangle
Use Inverse Sine to Determine an Angle in a Right Triangle
Use Tangent to Determine The Length of an Adjacent Side of a Right Triangle
Use Cosine to Determine The Length of a Hypotenuse of a Right Triangle
Use Sine to Determine The Length of a Hypotenuse of a Right Triangle
Use Inverse Sine to Determine an Angle in a Right Triangle
Use Inverse Cosine to Determine an Angle in a Right Triangle
Use Inverse Tangent to Determine an Angle in a Right Triange
Solve a Right Triangle Given an Angle and the Hypotenuse
Solve a Right Triangle Given an Angle and a Leg
Find the Reach of a Ladder - Right Triangle Application
Solving Right Triangles:  Part 2:  Applications
Ex: Find Height of Building Using Angle of Elevation and Angle of Depression
Determining an angle and other trig function values given a single trig function value
Ex: Solve a Right Triangle Using Inverse Trigonometric Functions

Radian Measure and Applications or Radian Measure

Radian Measure
Ex:  Converting Angles in Degree Measure to Radian Measure
Ex:  Convert Angles in Radian Measure to Degree Measure
Ex:  Determining Coterminal Angles in Radian Measure
Ex:  Determine Exact Trig Function Values With the Angle in Radians Using the Unit Circle
Ex:  Determine Exact Trig Function Values With the Angle in Radians Using Reference Triangles
Ex:  Determine Angles that have the Same Trig Function Value on the Interval [0, 360)
Arc Length and Area of a Sector
Ex:  Arc Length and Application of Arc Length
Ex:  Determine Arc Length of the Earth
Ex: Find the Angle that Subtends a Given Arc Length
Ex:  Area of a Sector and Area Bounded by a Chord and Arc
Linear Velocity and Angular Velocity
Ex:  Determine the Number or Revolutions Per Second of a Car Tire
Ex:  Determine Angular and Linear Velocity

Graphing Trigonometric Functions

Graphing the Sine and Cosine Functions
Ex:  Graph the Sine Function Using the Unit Circle
Animation:  Graphing the Sine Function Using the Unit Circle
Animation:  Graphing the Cosine Function Using the Unit Circle
Graphing the Tangent Function
Ex:  Graphing the Tangent Function Using the Unit Circle and the Reciprocal Identity
Animation:  Graphing the Tangent Function Using the Unit Circle
Graphing the Cosecant and Secant Functions
Ex:  Graphing the Secant Function Using the Cosine Function
Ex:  Graphing the Cosecant Function Using the Sine Function
Ex:  Domain of the Secant and Cosecant Functions Using the Unit Circle
Graphing the Cotangent Function
Graphing Cosine, Sine, and Tangent on the TI84
Graphing Secant, Cosecant, and Cotangent on the TI84

Graphing Transformations of Trigonometric Functions

Amplitude and Period of Sine and Cosine
Horizontal and Vertical Translations of Sine and Cosine
Characteristics of a Transformation of the Cosine Function (Reflection, No Vertical Shift)
Characteristics of a Transformation of the Cosine Function (4 Transformations with Reflection)
Characteristics of a Transformation of the Sine Function (4 Transformations with Reflection)
Graphing Sine and Cosine with Various Transformations
Animation: 
Transformations of Sine in the form y = Asin(B(x – D)) + C
Ex: Find the Maximum and Minimum of a Trig Function Using a Graphing Calculator
Ex:  Describe the Transformations of a Trig Function from a Graph
Determine the Equation of a Sine Transformation From a Description
Determine the Equation of a Sine Function in the Form y=Asin(kx)
Graph a Transformation of The Cosine Function (B=1) (Pos A)
Graph a Transformation of The Cosine Function (B=1) (Neg A)
Graph a Transformation of The Cosine Function y=Acos(B(x-D))+C  (Neg A)
Graph a Transformation of The Cosine Function y=Acos(B(x-D))+C  (Pos A)
Graph a Transformation of The Sine Function y=Asin(B(x-D))+C  (Neg A)
Graph a Transformation of The Sine Function y=Asin(B(x-D))+C  (Pos A)
Ex 1:  Graphing a Transformation of Sine and Cosine
Ex 2:  Graphing a Transformation of Sine and Cosine
Ex 3:  Graphing a Transformation of Sine and Cosine
Ex 4:  Graphing a Transformation of Sine and Cosine
Ex: Find the Equation of a Transformed Cosine Function - Form: Acos(Bx)
Ex: Find the Equation of a Transformed Sine Function - Form: Asin(B(x-D))
Ex: Find the Equation of a Transformed Cosine Function - Form: Acos(Bx)+C
Determining the Equations of Sine and Cosine Functions
Ex:  Determine the Equation of a Transformed Sine Function From a Graph
Ex:  Find a Trig Function from a Table of Values - No Phase Shift
Ex:  Find a Trig Function from a Table of Values - With Phase Shift
Ex:  Model Daily Temperatures Using a Trig Function
Graphing Tangent and Cotangent over different Periods
Ex: Trigonometric Model -Displacement of a Mass on a Spring
Ex:  Graphing a Transformation of Cosecant Function
Ex:  Graphing the Tangent Function Over a Different Period
Ex:  Graphing a Transformation of the Cotangent Function
Ex:  Graph a Transformation of the Tangent Function (Period and Horizontal Shift)
Ex:  Graph a Transformation of a Secant Function (Period and Horizontal Shift)
Ex: Find the Equation of a Transformed Cosecant Function From The Graph
Ex: Find the Equation of a Transformed Secant Function From The Graphh

Reciprocal, Quotient, Negative, and Pythagorean Trigonometric Identities

Properties of Trig Functions:  Domain, Range, and Sign in each QuadrantFind Excluded Values of the Domain of Tangent and Cotangent
Fundamental Identities:  Reciprocal, Quotient, Pythagorean
Find an Angle That Shows an Equation is Not an Identity (csc and cot)
Find an Angle That Shows an Equation is Not an Identity (sine and cosine)
Cofunction Identities
Cofunction Identities for Sine, Tangent, and Cosecant
Example:  Verify Pythagorean Identities For a Specific Angle
Negative Angle identities
Ex 1: Simplify a Trigonometric Expression Using Negative Angle Identities
Ex 2: Simplify a Trigonometric Expression Using Negative Angle Identities
Even and Odd Trigonometric Identities
Ex:  Even and Odd Trigonometric Identities
Verifying Identities using Basic Identities
Simplify Trigonometric Expressions (Basic Products)
Simplify Trigonometric Expressions (Basic Quotients)
Simplify Trigonometric Expressions (Quotients I)
Simplify Trigonometric Expressions (Quotients IIA)
Simplify Trigonometric Expressions (Quotients IIB)
Simplify Trigonometric Expressions (Sum of Fractions: sine and cosine)
Simplify Trigonometric Expressions (Sum of Fractions: sec and tan)
Simplify Trigonometric Expressions: (Pythagorean Identities)
Ex 1:  Simplify a Basic Trigonometric Expression
Ex 2:  Simplify Trigonometric Expressions
Ex 3:  Simplify a Trigonometric Expression
Ex 4:  Simplify Trigonometric Expressions - Squared Terms
Ex 1: Simplifying a Trigonometric Expression
Ex 2: Simplifying a Trigonometric Expression
Ex 3: Simplifying a Trigonometric Expression
Ex 4: Simplifying a Trigonometric Expression
Ex 5: Simplifying a Trigonometric Expression
Ex: Simplify a Trigonometric Expression: 1/(1+trig)-1/(1-trig)
Ex: Simplify a Trigonometric Expression: (trig-trig)/(trig-trig^2)
Ex: Simplify a Trigonometric Expression: (trig+trig*trig)/(trig+trig*trig)
Ex: Simplify a Trigonometric Expression: (trig+-trig)/(1+trig) (A)
Ex: Simplify a Trigonometric Expression: (trig+-trig)/(1+trig) (B)
Ex: Simplify a Trigonometric Expression: (trig+-trig)/(1+trig) (A)
Ex: Simplify a Trigonometric Expression: (trig+-trig)/(1+trig) (B)
Ex: Simplify a Trigonometric Expression: (2-trig^2)/trig^2 (A)
Ex: Simplify a Trigonometric Expression: (2-trig^2)/trig^2  (B)

Sum and Difference Trigonometric Identities

Sum and Difference Identities for Cosine
Sum and Difference identities for Sine
Sum and Difference Identities for Tangent
Ex:  Simplify a Trig Expression Using the Sum and Difference Identities
Ex:  Evaluate a Trig Expression Using the Sum and Difference Identities
Ex:  Using The Sum and Difference Identity to Determine a Sine Function Value
Ex:  Using The Sum and Difference Identity to Determine a Cosine Function Value
Ex:  Using The Sum and Difference Identity to Determine a Tangent Function Value
Ex: Write the Cosine of a Sum using Sine and Cosine Using a Sum and Difference Angle Identity
Ex: Simplify a Trig Expression with Tangent Using a Sum or Difference Angle Identity
Ex: Simplify a Trig Expression with Cosecant Using a Sum or Difference Angle Identity
Ex: Find sin(a+b) and cos(a-b) given sin(a) and cos(b)
Sum and Difference Identities: Evaluate sin(x-90) and cos(180+x)
Sum and Diff Identities: Find sin(A+B) and sin(A-B) given sin(A) and sin(B)
Ex: Simplify sin(x+y) - sin(x-y) Using Sum and Difference Identities
Ex: Simplify Tan(pi/2 - u) Using Sine and Cosine Difference Identity
Ex: Solve a Trigonometric Equation Using a Sum and Difference Angle Identity

 Double Angle Trigonometric Identities

Double Angle Identities
Ex:  Simplify and Evaluate a Trig Expression Using a Double Angle Identity
Ex 1:  Determine Double Angle Trig Function Values Given Information
Ex 2:  Determine Double Angle Trig Function Values Given Information
Simplify Trig Expression (1-cos(2x))/sin(x) - Find an Identity
Simplify Trig Expression (cos x)^4-(sin x)^4
Simplify Trig Expression: Quotient with Sines and Cosines and Double Angle
Trig Identities: Find an Identity for (2cos(2x))/(sin(2x)) (Double Angle)

Half Angle Trigonometric Identities

Half Angle Identities
Verifying Identities:  Sum, Difference, Double, and Half Angle Identities
Ex:  Rewrite a Trig Expression Using a Half Angle Identity
Half Angle Identity:  Determine cos(pi/12)=cos(15)
Half Angle Identity:  Determine sin(pi/8)=sin(22.5)
Half Angle Identity: Find cos(u/2) Given cot(u)
Half Angle Identity: Find cos(u/2) Given csc(u)
Half Angle Identity: Find sin(u/2) Given sin(u)
Half Angle Identities: Find sin(u/2), cos(u/2), tan(u/2)  Given cos(u) Q3
Half Angle Identities: Find sin(u/2), cos(u/2), tan(u/2)  Given sin(u) Q3
Half Angle Identities: Find sin(u/2), cos(u/2), tan(u/2)  Given tan(u) Q4
Ex:  Determine a Cosine Function Value Using a Half Angle Identity (Radians)
Ex:  Determine a Cosine Function Value Using a Half Angle Identity (Degrees)
Ex:  Determine a Cosine Function Value Using a Alternative Half Angle Identity (Degrees)
Ex:  Determine a Sine Function Value Using a Half Angle Identity (Radians)
Ex:  Determine a Sine Function Value Using a Alternative Half Angle Identity (Radians)
Ex:  Determine a Sine Function Value Using a Half Angle Identity (Degrees)
Ex:  Determine a Sine Function Value Using a Alternative Half Angle Identity (Degrees)
Ex:  Determine a Tangent Function Value Using a Half Angle Identity
Ex:  Determine a Cosine Function Value Using a Half Angle Identity (Degrees)
Ex:  Determine a Cosine Function Value Using a Alternative Half Angle Identity (Degrees)
Ex:  Determine a Sine Function Value Using a Half Angle Identity (Radians)
Ex:  Determine a Sine Function Value Using a Alternative Half Angle Identity (Radians)
Ex:  Determine a Sine Function Value Using a Half Angle Identity (Degrees)
Ex:  Determine a Sine Function Value Using a Alternative Half Angle Identity (Degrees)

Sum to Product and Product to Sum Trigonometric Identities

Sum to Product and Product to Sum Identities
Ex: Sum to Product Trigonometric Identity Involving Cosine
Ex: Sum to Product Trigonometric Identity Involving Sine
Ex: Product to Sum Trigonometric Identity Involving (sin(x)*sin(y) and cos(x)*cos(y))
Ex: Product to Sum Trigonometric Identity Involving (sin(x)*cos(y) and cos(x)*sin(y))
Ex: Simplify a Trig Expression Using Sum to Product Identities
Ex: Solve a Trigonometric Equation Using a Sum to Product Identity

Inverse Trigonometric Functions

Inverse Functions
Animation:  Illustrate why a function must be one-to-one to have an inverse function
Animation:  Illustrate why the domain must be restricted
Intro to the Inverse Functions of Sine, Cosine, and Tangent
Ex: Solve a Right Triangle Using Inverse Trigonometric Functions
Ex: Inverse Trig Function Application - Rocket Height
Evaluating Expressions and Solving Problems Using Inverse Sine, Cosine, and Tangent
Ex: Evaluate Basic Inverse Trig Expressions Involving Arccosine Using the Unit Circle
Ex:  Evaluate Basic Inverse Trig Expressions Involving Arcsine Using the Unit Circle
Evaluate Inverse Cosine Expressions Using the Unit Circle (Nice Values)
Evaluate Inverse Sine Expressions Using the Unit Circle (Nice Values)
Evaluate Inverse Tangent Expressions Using the Unit Circle (Nice Values)
Evaluate Inverse Cosine Expressions Using the Reference Triangles
Evaluate Inverse Sine Expressions Using the Reference Triangles
Evaluate Inverse Tangent Expressions Using the Reference Triangles
Ex:  Evaluate Expressions Involving Arctangent
Ex:  Evaluate Inverse Trig Expressions (Part 1)
Ex:  Evaluate Inverse Trig Expressions (Part 2)
Ex:  Evaluate Inverse Trig Expressions (Part 3)
Ex:  Evaluate Expression Involving Inverse Trig Functions (Part 1)
Ex:  Evaluate Expression Involving Inverse Trig Functions (Part 2)
Intro to the Inverse Functions of Cosecant, Secant, and Cotangent
Evaluate Inverse Cotangent Expressions Using the Unit Circle (Nice Values)
Evaluate Inverse Cosecant Expressions Using the Unit Circle (Nice Values)
Evaluate Inverse Secant Expressions Using the Unit Circle (Nice Values)
Evaluate Inverse Cosecant Expressions Using Reference Triangles
Evaluate Inverse Cotangent Expressions Using Reference Triangles
Evaluate Inverse Secant Expressions Using Reference Triangles
Evaluating Expressions Involving Inverse Cosecant, Secant, and Cotangent
Ex:  Evaluate Inverse Cosecant Without a Calculator
Ex:  Evaluate Inverse Secant Without a Calculator
Ex:  Evaluate an Inverse Cotangent Expression Using a Calculator
Ex:  Evaluate a Trig Expression with an Inverse Trig Function in Terms of u.
Ex:  Evaluate a Trigonometric Expression Containing an Inverse Trig Function - Double Angle
Ex:  Evaluate arccot(-3.6) Using a Calculator
Ex 1:  Evaluate tan(arcsin(-12/13))
Ex 2:  Evaluate sin(arctan(-7))
Ex 3:  Evaluate sin(arctan(u/3))
Inverse Trig Function Values of Trig Function Values Using Unit Circle (1st Quad)
Inverse Trig Function Values of Trig Function Values Using Reference Triangles  (1st Quad)
Trig Function Values of Inverse Trig Function Values Using Unit Circle (1st Quad)
Trig Function Values of Inverse Trig Function Values Using Reference Triangles (1st Quad)
Inverse Trig Function Values of Trig Function Values (Not Nice Angles)
Inverse Trig Function Values of Trig Function Values (Not Nice Angles, Neg)
Inverse Trig Function Values of Trig Function Values Using Unit Circle (Nice Angles A)
Inverse Trig Function Values of Trig Function Values Using Unit Circle (Nice Angles B)
Trig Function Values of Inverse Trig Function Values (Decimals)
Trig Function Values of Inverse Trig Function Values Using Unit Circle (Nice Values)
Inverse Trig Function Values of Trig Function Values Using Ref Triangles (Nice Angles A)
Inverse Trig Function Values of Trig Function Values Using Ref Tri (Nice Angles B)
Trig Function Values of Inverse Trig Function Values Using Reference Triangles (Not Q1)

Solving Trigonometric Equations

Ex:  Solve sin(x)=a  Without a Calculator
Ex:  Solve cos(x)=a  Without a Calculator
Ex:  Solve csc(x)=a  Without a Calculator
Ex:  Solve sec(x)=a  Without a Calculator
Ex:  Solve cot(x)=a  Without a Calculator
Ex:  Solve tan(x)=a  Without a Calculator
Solve Trigonometric Equations I
Solve Trigonometric Equations II
Solve Trigonometric Equations III
Solve Trigonometric Equations IV
Solve Trigonometric Equations V
Solve Trigonometric Equations VI
Ex: Solve sin(x)=a Using a Calculator (positive a)
Ex: Solve cos(x)=a Using a Calculator (negative a)
Ex: Solve sin(x)=a Using a Calculator (negative a)
Ex:  Solve cos(x)=a  on [0,2pi) with a Calculator  (positive a)
Ex:  Solve tan(x)=a  on [0,2pi) with a Calculator  (negative a)
Ex:  Solve Trig Equation:  sin(x) = cos(x)
Solve Basic Trig Equations in Radians: tan(x)+1=0 , csc(x)-2=0 (Unit Circle)
Solve  Trig Equation by Factoring: 2sin^2(x)-sin(x)-1=0 (Radians)
Cofunction Identities – Solving Trigonometric Equations
Solve Applications with Trigonometric Equations
Ferris Wheel Trigonometry Problem
An Equation for Simple Harmonic Motion of a Spring
Ex:  Solve a Trig Equation with an Inverse Trig Function
Ex: Solve a Trig Equation for a Variable
Ex : Solve a Trigonometric Equation Using a Graphing Calculator
Ex: Solve a Trigonometric Equation Using a Calculator (sin(x)=-0.36)
Ex 1:  Solving a Trigonometric Equation
Ex 2:  Solving a Trigonometric Equation
Ex 3:  Solving a Trigonometric Equation
Ex 4:  Solving a Trigonometric Equation Using a Trig Substitution and Factoring
Ex 5:  Solving a Trigonometric Equation Using Factoring
Ex:  Solve a Trigonometric Equation Using the Quadratic Formula
Ex 1: Solve a Trigonometric Equation Using a Double Angle Identity Substitution
Ex 2: Solve a Trigonometric Equation Using a Double Angle Identity Substitution
Solve A Trig Equation with a Double Angle (sin(2x)) radians
Solve A Trig Equation with a Triple Angle (cos(3x)) radians
Ex 1:  Solving a Trig Equation with a Multiple Angle
Ex 2:  Solving a Trig Equation with a Multiple Angle
Solving Trigonometric Equations Using Substitution for Angles
Solving Trigonometric Equations Using Identities and Substitution
Ex 1:  Solve a Basic Trig Equation Using the Unit Circle and Reference Triangles
Ex 2:  Solve a Basic Trig Equation Using the Unit Circle and Reference Triangles
Ex 3:  Solve a Basic Trig Equation Using the Unit Circle and Reference Triangles
Ex 1:  Solve a Trig Equation with Rounded Radian Solutions – Angle Substitution
Ex 2:  Solve a Trig Equation with Rounded Radian Solutions - Angle Substitution
Ex 3:  Solve a Trig Equation with Rounded Radian Solutions - Angle Substitution with Pi
Ex: Solve a Trig Equation Containing Cosecant with Rounded Radian Solutions – Angle Substitution
Ex: Solve a Factorable Trig Equation Using Radians - Exact Solutions
Ex: Solve a Factorable Trig Equation Requiring Substitution Using Radians - Exact Solutions
Ex: Solve a Factorable Trig Equation with Exact and Rounded Radian Solutions
Ex:  Solve a Factorable Trig Equation with Rounded Radian Solutions - Quadratic Form
Ex 1:  Solve a Trig Equation Using a Double Angle Identity
Ex 2:  Solve a Trig Equation Using a Double Angle Identity
Ex:  Solve 1.2cos(x)=sin(2x)
Ex 1:  Solve a Trig Equation Contain Inverse Trig Functions
Ex 2:  Solve a Trig Equation Contain Inverse Trig Functions
Ex:  Solve a Trig Equation for One Variable in Terms of Another
Ex:  Solve a Right Triangle Given the Length of Two Sides
Ex:  Determine the Height of an Object Using a Trig Equation
Ex 1:  Determine an Unknown Length Using Right Triangle Trigonometry
Ex 2:  Determine an Unknown Length Using Right Triangle Trigonometry
Ex 3:  Determine an Unknown Length Using Right Triangle Trigonometry

Solving Triangles Using the Law of Sines and Law of Cosines

 The Law of Sines:  The basics
The Law of Sines:  The ambiguous case
Use the Law of Sines to Determine a Side Length (AAS)
The Law of Sines - No Solution (SSA)
The Law of Sines - One Solution (SSA)
oThe Law of Sines - Two Solutions (SSA)
Use the Law of Sines to Find the Length of a Side of a Triangle After Finding 3rd Angle
Use the Law of Sines Twice to Find the Length of a Side of a Triangle (Lake Problem)
The Area of a Triangle Using Sine
The Area of a Triangle Using Heron’s Formula
The Law of Sines:  Applications I
The Law of Sines:  Applications 2
Example:  Solve a Triangle Using the Law of Sines (given two sides and an angle)
Example:  Solve a Triangle Using the Law of Sines (given two angles and one side)
Example 1:  Determine an Unknown Length Using the Law of Sines
Example 2:  Determine an Unknown Length Using the Law of Sines
Example 3:  Determine an Unknown Length Using the Law of Sine (airplane problem)
Ex: Law of Sine to Determine a Height of a Building Given Two Angles of Elevation
Ex: Law of Sine to Determine a Height of a Satellite Given Two Angles of Elevation
The Law of Cosines
Solve a Triangle Using the Law of Cosines and the Law of Sines
Use the Law of Cosines to Find the Length of a Side of a Triangle (SAS)
Use the Law of Cosines to Find the Measure of an Angle of a Triangle (SSS)
The Law of Cosines:  Applications
Example 1:  Application of the Law of Cosines  (width of lake)
Example 2:  Application of the Law of Cosines  (distance plane travels)
Example 3:  Application of the Law of Cosines  (diagonal of parallelogram)
Example 4:  Application of the Law of Cosines (measure of an angle)
Ex: Find the Area of a Quadrilateral Using Law of Cosines and Heron's Formula
Ex:  Find Length of a Support Wire on a Hill Using the Law of Cosines
Ex: Law of Cosine Application (Cable Car to Top of Mountain)

Vectors and Vector Applications

Introduction to Vectors
Vector Operations
Ex: Find the Sum of Two Vectors From a Graph (2 Dimensions)
Ex: Geometric Interpretation of Vector Arithmetic
Ex: 2D Vector Scalar Multiplication
Ex: Find the Unit Vector Given the Graph of a Vector in 2D
Ex: Find the Difference of Two Vectors in Component Form
Ex: Find the Sum of Two Vectors Given in Linear Combination Form
Ex: Find the Difference of Two Vector Given in Linear Combination Form
Ex: Find the Difference of Scalar Multiples of Vectors in 2D
Ex 1: Fine a Vector in Component Form Given an Angle and the Magnitude (30)
Ex 2: Fine a Vector in Component Form Given an Angle and the Magnitude (45)
Ex 3: Fine a Vector in Component Form Given an Angle and the Magnitude (60)
Ex 4: Fine a Vector in Component Form Given an Angle and the Magnitude (90)
Ex 5: Fine a Vector in Component Form Given an Angle and the Magnitude (180)
Ex: Find the Difference of Scalar Multiples of Vectors in 2D
Ex: Find the Magnitude of The Difference of Two Vectors and The Difference of Two Magnitudes
Applications of Vectors
Ex:  Write a Vector as a Combination of Two Vectors
Ex:  Find the Net Force of Three Vectors and the Opposite Force
Ex:  Find the Coordinates of a Rotated Point Using Vectors
Ex:  Direction and Speed of a Plane in the Wind Using Vectors
Ex: Vector App:  Find an Airplane Direction In  The Wind To Fly Due North
Vector App:  Find the Direction of a Ball Thrown From a Car
Ex: Vector App - Find the Resultant Vector of a 5 Direction Walk
Ex: Vector App - Find the Resultant Vector of a 2 Direction Walk
Vector Application Using Law of Sines: Find Direction Angle Needed to Fly Due North in Wind
Vector App Using Law of Sines and Cosines: Find  Angle Off Course and Velocity of a Plane in Wind

Polar Equations

Polar Coordinates
Example:  Identify 4 Possible Polar Coordinates for a Point Using Degrees
Polar Coordinates of a Point 4 Ways (Degrees)
Example:  Identify 4 Possible Polar Coordinates for a Point Using Radians
Animation:  Rectangular and Polar Coordinates
Example:  Convert a Point in Rectangular Coordinates to Polar Coordinates Using Degrees
Example:  Convert a Point in Rectangular Coordinates to Polar Coordinates Using Radians
Example:  Convert a Point in Polar Coordinates to Rectangular Coordinates
Converting Polar Equations to Rectangular Equations
Cartesian and Polar Equation of a Circle from a Graph - Center (0,0)
Convert a Polar Equation to a Polar Equation (Horizontal and Vertical Line)
Ex:  Write a Polar Equations of a Line as a Cartesian (Rectangular) Equations
Ex:  Write the Standard Form of a Circle From a Graph
Ex:  Find the Rectangular and Polar Equation of a Circle From a Graph
Ex:  Find the Polar Equation of a Circle With Center at the Origin
Ex:  Find the Polar Equation for a Horizontal Line
Ex:  Find the Polar Equation for a Line
Ex:  Find the Polar Equation for a Parabola
Ex:  Find the Rectangular Equation of a Circle from a Polar Equation
Ex:  Convert a Rectangular Equation to a Polar Equation
Graph Polar Equations I
Graph Polar Equations II
Animation:  Graph Polar Equations
Graphing Polar Equations on the TI84 Graphing Calculator

Complex Numbers

Complex Numbers
Complex Number Operations
Trigonometric Form of Complex Numbers
Product and Quotient of Complex Numbers in Trig Form
DeMoivre’s Theorm:  Powers of Complex Numbers in Trig Form
Ex: Convert a Complex Number in Cartesian Form to Exponential Form
Ex: Convert a Complex Number in Exponential Form to Cartesian Form
Ex: Raise a Complex Number in Polar Form to a Power - Demoivre's Theorem
Ex: Raise a Complex Number in Polar Form to a Power Using Exponential Form
Ex 1: Raise a Complex Number in Cartesian Form to a Power - Demoivre's Theorem
Ex 2: Raise a Complex Number in Cartesian Form to a Power - Demoivre's Theorem
Roots of Complex Numbers
Ex: Find the Square Root of a Complex Number (DeMoivre's Theorem)

Parametric Equations


Introduction to Parametric Equations
Graphing Parametric Equations in the TI84
Converting Parametric Equation to Rectangular Form
Ex 1: Write Parametric Equations as a Cartesian Equation
Ex 2: Write Parametric Equations as a Cartesian Equation
Ex 3: Write Parametric Equations as a Cartesian Equation
Ex 4: Write Parametric Equations as a Cartesian Equation
Ex: Parametric Equations for an Ellipse in Cartesian Form
Ex: Find Parametric Equations For Ellipse Using Sine And Cosine From a Graph
Find the Parametric Equations for a Line Segment Given an Orientation
Ex 1:  Find the Parametric Equations for a Lissajous Curve
Ex 2:  Find the Parametric Equations for a Lissajous Curve
Ex 3:  Find the Parametric Equations for a Lissajous Curve
Ex 4:  Find the Parametric Equations for a Lissajous Curve
Ex:  Point on a Spoke of a Rotating Wheel - Find the Radius

Graphing Calculator


Ex:  Estimating Square Roots with a Calculator
Determine Trigonometric Function Values on the Calculator
Graphing Cosine, Sine, and Tangent on the TI84
Graphing Secant, Cosecant, and Cotangent on the TI84
Ex:  Evaluate an Inverse Cotangent Expression Using a Calculator
Ex:  Evaluate arccot(-3.6) Using a Calculator
Ex 1:  Solving a Trig Equation Using a Calculator
Ex 2:  Solving a Trig Equation Using a Calculator
Graphing Polar Equations on the TI84 Graphing Calculator

Make a free website with Yola