1. 14.7 Solving Trig Equations

2. Example 7-1a Find all solutions offor the interval 0  <   360 . Original equation Solve for 0. Distributive Property Divide each side by –1. Simplify. Factor. Example:

3. Example 7-1a Now use the Zero Product Property. Answer: The solutions are 30°, 150°, and 270°. or

4. Example 7-1a Find all solutions of for the interval 0  <   2 . Original equation Solve for 0. Factor Example:

5. Example 7-1a Use the Zero Product Property. Answer: The solutions are or

6. Find all solutions of each equation for the given interval. a. b. Example 7-1b Answer:  Answer: More problems:

7. Example 7-2a Solvefor all values of if is measured in radians. Original equation Subtract Factor. or Zero Product Property Solve. Example:

8. Example 7-2a Look at the graph ofto find solutions of The solutions areand so on, and so on.

9. Example 7-2a The only solution in the interval 0 toareand The period of the sine function isradians. So the solutions can be written as and where k is any integer. Similarly, the solutions for

10. Example 7-2a Answer: The solutions are and

11. Example 7-2a Solvefor all values ofifis measured in degrees. Original equation Solve for 0. Factor. Example:

12. Example 7-2a Solve forin the interval of or Answer: The solutions are

13. a. Solvefor all values ofifis measured in radians. b. Solvefor all values ofif is measured in degrees. Example 7-2b Answer: There is more:

14. Example 7-3a Solve Original equation Multiply. Factor. Example:

15. Example 7-3a or

16. Example 7-3a Thus,is not a solution. is undefined. Answer: The solution is Check

17. Example 7-3b Solve Answer: The solution is. Your turn:

18. Example 7-4a Solve Subtract 1 and add to each side. Original equation Multiply each side by 4. Factor. Example:

19. Example 7-4a or is undefined for Answer: The solutions are and

20. Example 7-4b Solve Answer: Your turn again: