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Angles and Right Triangles

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

The Unit Circle

Determining Trigonometric Function Values and Angles

Determine an Angle in Standard Position That Passes Through a Given Point (Nice Angles in Degrees)
Determine an Angle in Standard Position That Passes Through a Given Point (Nice Angles in Radians)
Determine an Angle in Standard Position That Passes Through a Given Point (Messy Angles in Degrees)
Determine an Angle in Standard Position That Passes Through a Given Point (Messy Angles in Radians)
Robot Maze: Determine a Path Through a Maze Using Trigonometry and Geometry
Use a Trigonometric Function to Determine a Projectile angle to Hit a Target

Solving Right Triangles

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
Given the Arc Length of a Circle, Find the Circumference and Area
Determine the Distance Between Two Cities Using Arc Length
Ex: Area of a Sector and Area Bounded by a Chord and Arc
Area of Sector: Find the Area Swept by a Windshield Wiper Blade
Linear Velocity and Angular Velocity
Angular Velocity and RPMs Going 50 MPH
Determine Angular Velocity, Linear Velocity, and Distance: Ladybug of a Record
Determine Angular Velocity, Linear Velocity, and Distance: Bicycle Wheel
Angular Velocity and Linear Velocity: Planetary Ring
Angular Velocity and Linear Velocity: A Hamster Running in a Wheel
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
Animations of the Graphs of Cosine and Sine Using the Unit Circle (Desmos)
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 Cosine, Sine, and Tangent Using Desmos (Degrees)
Graphing Cosine, Sine, and Tangent Using Desmos (Radians)
Graphing the secant function using Desmos (degrees)
Graphing the secant function using Desmos (radians)
Graphing the cosecant function using Desmos (degrees)
Graphing the cosecant function using Desmos (radians)
Graphing the cotangent function using Desmos (degrees)
Graphing the cotangent function using Desmos (radians)

Graphing Transformations of Trigonometric Functions

Modeling with Trigonometric Functions

Ex: Model Daily Temperatures Using a Trig Function
Model Daily Temperature Using a Cosine Transformation
Ex: Trigonometric Model -Displacement of a Mass on a Spring
Modeling Daylight Hours With a Sine Function Value: Points of Intersection Using Desmos
Model the Amount of Sea Ice Using a Transformation of the Cosine Function
Model the Length of a Ladder Over a Fence using a Trignometric Function

Reciprocal, Quotient, Negative, and Pythagorean Trigonometric Identities

Sum and Difference Trigonometric Identities

Double Angle Trigonometric Identities

Trigonometric 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

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
Evaluate Trigonometric Composite Function Expressions with Variables

Inverse Trigonometric Functions

Solving Trigonometric Equations

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)
The 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
New Version: The Law of Cosines
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)
Law of Sines: Determine The Number of Possible Triangles Given SSA
Law of Sines and Right Triangle Trigonometry:
Distance and Height of a Satellite
Law of Sines and Right Triangle Trigonometry:
Distance and Height of a UFO

Vectors and Vector Applications

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
Vector App: Find the Horizontal and Downward Force on a Lawnmower Handle
Vector App: Find the Eastern and Southern Displacement of a Walk
Find the Horizontal and Vertical Components of a Velocity Vector
Find the Resultant Force and Direction of 4 Force Vectors

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)
Complex Solutions (Roots) of Complex Number Using Exponential (Euler) Form: Z^2=2i
Complex Solutions (Roots) of Complex Number Using Exponential (Euler) Form: Z^2=-2+2sqrt(3)i
Complex Solutions (Roots) of Complex Number Using Exponential (Euler) Form: Z^3=8i
Complex Solutions (Roots) of Complex Number Using Exponential (Euler) Form: Z^4=-72+72sqrt(3)i
Complex Solutions (Roots) of Complex Number Using Exponential (Euler) Form: Z^4=-64

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

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