Reciprocal, Quotient, Negative, and Pythagorean Trigonometric Identities
Properties
of Trig Functions: Domain, Range, and
Sign in each Quadrant
Fundamental
Identities: Reciprocal, Quotient,
Pythagorean
Cofunction Identities
Example: Verify Pythagorean Identities For a Specific
Angle
Negative
Angle identities
Even
and Odd Trigonometric Identities
Ex: Even and Odd Trigonometric Identities
Verifying
Identities using Basic 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
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
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
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
Ex: Determine a Cosine Function Value Using a
Half Angle Identity
Ex: Determine a Sine Function Value Using a Half
Angle Identity
Ex: Determine a Tangent Function Value Using a
Half Angle Identity
Sum to
Product and Product to Sum Identities
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
Evaluating
Expressions and Solving Problems Using Inverse Sine, Cosine, and Tangent
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
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))
Solving Trigonometric Equations
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 Trig Equation: sin(x) = cos(x)
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
1: Solving a Trig Equation Using a
Calculator
Ex
2: Solving a Trig Equation Using a
Calculator
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
1: Solving a Trig Equation with a
Multiple Angle
Ex
2: Solving a Trig Equation with a
Multiple Angle
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 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
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)
The Law
of Cosines
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)
Vectors and Vector Applications
Introduction
to Vectors
Vector
Operations
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
Polar Equations
Polar
Coordinates
Example: Identify 4 Possible Polar Coordinates for a
Point Using 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
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
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
