# Proving/Verifying and Using Trig Identities

## What you'll learn

- How to Prove the Reciprocal and Quotient Identities
- How to Simplify Trig Expressions Using the Reciprocal and Quotient Identities
- How to Prove of The Odd and Even Trig Identities
- How to Verify Trig Identities Using the Odd and Even Trig Identities
- How to Prove the Cofunction Trig Identities
- Verifying Trig Identities Using the Cofunction Trig Identities
- How to Prove the Pythagorean Trig Identities
- How to Simplify Trig Expressions Using the Pythagorean Trig Identities
- How to Verify Trig Identities Using the Pythagorean Trig Identities
- How to Derive the Sum and Difference Trig Formulas
- How to Verify Trig Identities Using the Sum and Difference Formulas
- How to Find the Exact Value of Trig Functions Using the Sum Identities
- How to Prove the Double-Angle Formulas
- How to Simplify Trig Expressions Using the Double Angle Identities
- How to Prove the Power Reducing and Half-Angle Formulas
- How to Simplify Trig Expressions Using the Power Reducing Identities
- Using the Half Angle Identities to Find the Exact Value of Trig Expressions
- How to Prove the Product-to-Sum Formulas
- How to Prove the Sum-to-Product Formulas
- How to Use the Product-to-Sum Identities to Rewrite Trig Expressions
- How to Use the Sum-to-Product Identities to Solve Trig Equations
- Prove that a Trig Equation is NOT an Identity

## Requirements

- Algebra

## Description

This course is all about Proving/Verifying and Using Trig Identities.

Upon completing this course, you will understand how to prove the Reciprocal and Quotient Identities, Odd and Even Identities, Cofunction Identities, Pythagorean Identities, Sum and Difference Formulas, Double-Angle Identities, Power Reducing Identities, Half-Angle Identities, Product-to-Sum Formulas, and Sum-to-Product Formulas.

You will be able to use the above identities to verify other trig Identities, rewrite trig expressions, find the value of trig expressions, and solve trig equations.

Finally, you will understand how to prove that a trig equation is NOT an identity.

Section 1: The Reciprocal and Quotient Identities

Proof of the Reciprocal and Quotient Identities

Simplifying Trig Expressions Using the Reciprocal and Quotient Identities

The Reciprocal and Quotient Identities (Quiz)

Section 2: The Odd and Even Trig Identities

Proof of the Odd and Even Trig Identities

Verifying Trig Identities Using the Odd and Even Trig Identities

The Odd and Even Identities (Quiz)

Section 3: The Cofunction Trig Identities

Proof of the Cofunction Trig Identities

Verifying Trig Identities Using the Cofunction Trig Identities

Section 4: The Pythagorean Trig Identities

Proving the Pythagorean Trig Identities

Simplifying Trig Identities Using the Pythagorean Identities

Verifying Trig Identities Using the Pythagorean Identities

The Pythagorean Identities (Quiz)

Extra: Overview of Concepts (Hand-Written)

Extra: Tons of Problems Solved, Showing All Steps (Hand-Written)

Section 5: The Sum and Difference Formulas

Deriving the Sum and Difference Formulas for Sine and Cosine

Proving the Sum and Difference Formulas for Tangent and Cotangent

Verifying Trig Identities Using the Sum and Difference Formulas

Finding the Exact Value of Trig Functions Using the Sum Identities

The Sum and Difference Formula (Quiz)

Extra: Overview of Concepts (Hand-Written)

Extra: Tons of Problems Solved, Showing All Steps (Hand-Written)

Section 6: The Double Angle Formulas

Proving the Double Angle Identities

Verifying Trig Identities Using the Double Angle Formulas

The Double-Angle Identities (Quiz)

Extra: Overview of Concepts (Hand-Written)

Extra: Tons of Problems Solved, Showing All Steps (Hand-Written)

Section 7: The Power Reducing and Half-Angle Identities

Proving the Power Reducing and Half-Angle Identities

Using the Power-Reducing Identities to Rewrite Trig Expressions

Using the Half Angle Identities to Find the Exact Value of Trig Expressions

Using the Half-Angle Trig Identities to Find the Exact Value

The Power Reducing and Half-Angle Identities (Quiz)

Extra: Overview of Concepts (Hand-Written)

Extra: Tons of Problems Solved, Showing All Steps (Hand-Written)

Section 8: The Product-to-Sum Formulas

Proving the Product-to-Sum Trig Formulas

Using the Product-to-Sum Identities to Rewrite Trig Expressions

The Product-to-Sum Formulas (Quiz)

Section 9: The Sum-to-Product Formulas

Proving the Sum to Product Trig Formulas

Using the Sum-to-Product Identities to Solve Trig Equations

The Sum-to-Product Formulas (Quiz)

Section 10: Disproving Identities

Proving that a Trig Equation is NOT an Identity

Disproving Identities (Quiz)

For each topic, you are given:

1. An reading (attached as a resource) explaining concepts, details, and the example that is used in the video.

2. A video showing a visual of the example in the reading.

If you watch each video and follow the associated reading, you will have a good understanding for proving/verifying and using trig Identities.

I hope that I can assist you on your math journey!

Sincerely,

MathAngel369

## Who this course is for:

- Students taking a trigonometry class

## Instructor

My name is Angela Morgan and I am the creator of MathAngel369. I hold a Masters Degree in Applied Mathematics (2018) and a Bachelors Degree in Mathematics, minor in Chemistry (2008).

I have a career as a Lecturer in Mathematics (University); teaching since Fall of 2019.

Outside of work, I record math videos in my home studio so I can serve as a resource for others who wish to learn math on their own time.

In addition to my videos, I provide math discussions that include details and concepts of the examples discussed in my videos.

Lastly, I include hand written notes that I use to teach my college students. My notes contain an overview, concepts, and tons of additional problems solved, showing each step.

As a lecturer (2019-present), I have experience teaching traditional, online, and hybrid classes at the University level.

As a former Graduate Teaching Assistant (2017-2019), I have experience tutoring and teaching undergraduate students.

To be honest, I didn’t really learn math in school. During class, the lectures would go clean over my head. I had to teach myself and learn math alone.

On the upside to this, my struggles became my greatest strength because it helped me learn how to reach others who struggle in math the way I did.

I hope that my discussions, videos, and notes help you on your math journey!

Sincerely,

MathAngel369