1. PreCalculus 5-3 Solving Trigonometric Equation

2. Trigonometric Equations To solve trigonometric equations, we must solve for all values of the variable that make the equation true.

3. All the solutions for x can be expressed in the form of a general solution. x = is one of infinitely many solutions of y = sin x. π 6 x = + 2k π and x = + 2k π (k = 0, ±1, ± 2, ± 3,  ). 6 π 5π5π 6 sin x = is a trigonometric equation. x y 1 -19 π 6 -11 π 6 -7 π 6 π 6 5 π 6 13 π 6 17 π 6 25 π 6 -π-π -2 π -3 π π 2π2π 3π3π 4π4π y = Trigonometric Equations

4. 4 Find the general solution for the equation sec  = 2. All values of  for which cos  = are solutions of the equation. Two solutions are  = ±. All angles that are coterminal with ± are also solutions and can be expressed by adding integer multiples of 2π. π 3 π 3 The general solution can be written as  = ± + 2kπ. π 3 From cos  =, it follows that cos  = 1 sec  cos( + 2kπ) = π 3 -π-π 3 x y Q 1 P

5. Trigonometric Equations

6. Solve the equation

7. Trigonometric Equations

8. Solve the equation

9. Trigonometric Equations

11. Solve the equation

12. Trigonometric Equations Solve the equation

13. Trigonometric Equations Solve the equation

14. Trigonometric Equations

15. Solve the equation in the interval [0,2π)

16. Trigonometric Equations

17. Solve the equation

18. Trigonometric Equations

19. Solve the equation in the interval (6π,8π)

20. Trigonometric Equations

21. Solve the equation in the interval (4π,6π)

22. Trigonometric Equations

24. Solve the equation

25. Trigonometric Equations

27. Solve the equation in the interval (0,2π)

28. Trigonometric Equations

29. Find all solutions of the equation

30. Trigonometric Equations

32. Solve the equation

33. Trigonometric Equations Homework page 364 - 365 3, 5, 11, 15 21, 25, 27, 29, 33, 35, 53, 55, 67