1. Warm up If sin θ= and find the exact value of each function. 1.cos 2θ 2.sin 2θ 3.Use the half-angle identity to find the exact value of the function: cos

2. Lesson 7-5 Solving Trigonometric Equations Objective: To solve trigonometric equations and inequalities

3. A trigonometric equation is an equation that contains a trigonometric function. For example : To solve a trig equation, we use algebra to isolate the trig function on one side of the equal sign.

4. Example If the variable is not restricted there is an infinite number of solutions. If principal values are require then only answers in quadrants I and IV work.

5. Example Solve –Use the Pythagorean Identity factor the trinomial

6. Example sin x = cos x dividing each side by cos x produces a different trig function on the left. This is what you want. sin 2 x= sin x dividing this does not produce a new function. Because you lose the squared term you will miss one of the answers.

7. Practice Solve for principal values of x. Express solutions in degree.

8. Practice Solve (Hint: Factor by grouping)