About This Chapter
Trigonometric Identities - Chapter Summary
Use this chapter to solidify your understanding of basic trig identities. Through a series of short and informative video lessons, our instructors show you how to apply, prove and derive several types of identities, such as Pythagorean, reciprocal and half-angle identities. Studying this chapter can help you:
- Recognize the basic trig identities and their alternate forms
- Understand the applications the Pythagorean, reciprocal and double-angle identities
- Make calculations using half-angle, product-to-sum and sum-to-product identities
- Use the six sum and difference identities
- Prove and derive trig identities
Following each lesson is a short quiz to help you retain the information you've studied and practice solving trig identify problems on your own. If you need clarification on a particular trig identity topic, you can easily submit questions to our instructors, who are happy to assist you. To make your studying experience flexible and convenient, we've made the chapter available to access on any computer or mobile device.
1. List of the Basic Trig Identities
There are specific trig functions that have very special and very simple relationships with each other. Learn the main one and how you can use it to understand the others.
2. Alternate Forms of Trigonometric Identities
After watching this video lesson, you will know some of the alternate forms of the basic trigonometric identities. You will also learn how to use these alternate forms.
3. Pythagorean Identities: Uses & Applications
After watching this video lesson, you will be able to spot the Pythagorean identities when you see them. You will also learn how these identities can help you solve more complicated trig problems.
4. Reciprocal Identities: Uses & Applications
Trigonometry is full of identities, a set of which are called the reciprocal identities. Watch this video lesson to learn what they are and how you can use them to help you solve problems.
5. Double-Angle Identities: Uses & Applications
Watch this video lesson to learn how you can use the double-angle identities in trigonometry to help you prove and solve more complicated trigonometry problems.
6. Half-Angle Identities: Uses & Applications
After watching this video lesson, you will be able to use half-angle identities to help you simplify your trig problems and also to help you prove other trig statements.
7. Product-to-Sum Identities: Uses & Applications
After watching this video lesson, you will know what the four product-to-sum identities are. You will also know how they are used. You will also see two examples of problems.
8. Sum-to-Product Identities: Uses & Applications
In this video lesson, you will learn about the four sum-to-product identities for the sine and cosine functions. Learn how to go from the sum or subtraction of two functions to the product of two functions along with the two angles.
9. Applying the Sum & Difference Identities
Watch this video lesson to learn the six sum and difference identities for the trig functions of sine, cosine, and tangent. Also, learn how you can use them to your advantage when solving tough trig problems.
10. How to Prove & Derive Trigonometric Identities
After watching this video lesson, you will learn how some of our trigonometric identities are derived. You will also see how some identities naturally lead to the others.
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