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6.5 Basic Trigonometric IdentitiesPowerPoint Presentation

6.5 Basic Trigonometric Identities

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Trigonometric Identities

- Trigonometric identities are equations that are true for all values of the variable for which the equation is defined. They are most often used to simplify an expression.
- Algebraic rules are the same for trigonometric expressions, the notation is sometimes just slightly different.

Quotient Identities

- In Chapter 6 we introduced the Unit Circle & we also learned our first identities:

Reciprocal Identities

- We also learned the reciprocal identities.

Example #1

- Simplify the following expressions:
A) B)

Pythagorean Identities

- Using the Pythagorean Theorem & the Unit Circle, the Pythagorean Identities are created:

Pythagorean Identities continued…

Be very careful when using Pythagorean identities, the expressions must be squared:

Example #4

- Use the Quotient, Reciprocal, and Pythagorean identities to find the remaining 5 trigonometric functions.

Example #5

- Simplify the following expression.

This problem required first factoring the top and using the identity:

After the substitution, the bottom was factored and the top rearranged. Canceling like terms gives the answer shown.

Example #6

- Simplify the following expression.

Here the expression has a GCF factored out first. Then a substitution is made with this identity:

Then the reciprocal identity is used and like terms are canceled. Finally, the reciprocal identity is used again.

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