Pythagorean Trig Identities are derived from the unit circle and using the Pythagorean Theorem. They play an important role in Trigonometry, especially in Trigonometric proofs, and being able to verify identities.
Pythagorean Trig Identities
Verify Identities Using -Pyth. Trig Identities
Verifying Trig Identities
To verify a Trig Identity, you must show that both sides are equivalent statements. This can be done by simplifying one side to equal the other, or it can be done by simplifying both sides to end up with the same expression. I tend to start by looking for Pythagorean Trig Identities, if applicable. If not, I tend to write the trig functions in terms of sin and cos. Many can be done in multiple approaches.
Verify Trig Identities (Easy)
Verify Trig Identities (More Complex)
Sum and Difference Identities
The sum and difference identities can be useful to find exact values for angles that are not on the unit circle. There is a sum and difference identity for cosine, sine and tangent. The videos in this section show how to find exact values, as well as how to use the sum and difference identities in reverse.
Use Cos Sum and Difference Identities to Find Exact Value
Use Sine Sum and Difference Identities to Find Exact Value
Use Sum and Difference Identities to Rewrite as a Single Trig Expression
Use Tangent Sum and Difference Identities to Find Exact Value
Double Angle Identities
The double angle identities result from the sum identities when A = B. The videos will demonstrate how to use the double angle identities to find values. They also will demonstrate how to verify double-angle identities and how to simplify expressions with the double angle identities.
Use Double Angle Identities to Find Sin(2x) and Cos(2x)