2. Solving Trigonometric Equations
Skill 33

3. Objectives…
Use standard algebraic techniques to solve trigonometric equations.
Solve trigonometric equations of quadratic type.
Solve trigonometric equations involving multiple angles.
Use inverse trigonometric functions to solve trigonometric equations.

4. Introduction
To solve a trigonometric equation, use standard algebraic techniques…
Collect like terms
Factor
Isolate the trigonometric function

5. Example–Solving a Trigonometric Equation
Solve 2 sin x – 1 = 0.
Solution:
2 sin x – 1 = 0
2 sin x = 1
sin x =
Write original equation.
Add 1 to each side.
Divide each side by 2.

6. Example–Solving a Trigonometric Equation

7. Example–Solving a Trigonometric Equation

8. Example–Solving a Trigonometric Equation

9. Solution: 2 sin2 x – sin x – 1 = 0 (2 sin x + 1)(sin x – 1) = 0
Example–Factoring an Equation of Quadratic Type
Solution:
2 sin2 x – sin x – 1 = 0
(2 sin x + 1)(sin x – 1) = 0
2 sin x + 1 = 0 and sin x – 1 = 0
sin x = sin x = 1
Write original equation.

10. Example–Factoring an Equation of Quadratic Type

11. Functions Involving Multiple Angles
We can use trigonometric functions of multiple angles of the forms sin ku and cos ku. To solve equations.
First solve for ku
Then divide by k.

12. Example–Functions Involving Multiple Angles
Solution:
2 cos 3t – 1 = 0
2 cos 3t = 1
cos 3t =
Write original equation.
Add 1 to each side.
Divide each side by 2.

13. Example–Functions Involving Multiple Angles

14. Example–Solving by converting to quadratic

15. 33 Solving Trigonometric Equations
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