1. Objective: Develop basic trigonometric identities.

2.  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.

3.  In Chapter 6 we introduced the Unit Circle & we also learned our first identities:

4.  We also learned the reciprocal identities.

5.  Simplify the following expressions: A)B)

6. 

7.  Using the Pythagorean Theorem & the Unit Circle, the Pythagorean Identities are created:

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

9.  Simplify the following expressions. A) This problem utilizes two identities:

10.  Simplify the following expressions. B) Two identities are also used here:

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

15.  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.

16.  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.