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Mathematics LibreTexts

7.4E: Solving Trigonometric Equations (Exercises)

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Section 6.4 Exercises

Give all answers in radians unless otherwise indicated.

Find all solutions on the interval 0θ<2π.

1. 2sin(θ)=2

2. 2sin(θ)=3

3. 2cos(θ)=1

4. 2cos(θ)=2

5. sin(θ)=1

6. sin(θ)=0

7. cos(θ)=0

8. cos(θ)=1

Find all solutions.

9. 2cos(θ)=2

10. 2cos(θ)=1

11. 2sin(θ)=1

12. 2sin(θ)=3

Find all solutions.

13. 2sin(3θ)=1

14. 2sin(2θ)=3

15. 2sin(3θ)=2

16. 2sin(3θ)=1

17. 2cos(2θ)=1

18. 2cos(2θ)=3

19. 2cos(3θ)=2

20. 2cos(2θ)=1

21. cos(π4θ)=1

22. sin(π3θ)=1

23. 2sin(πθ)=1.

24. 2cos(π5θ)=3

Find all solutions on the interval 0x<2π.

25. sin(x)=0.27

26. sin(x)=0.48

27. sin(x)=0.58

28. sin(x)=0.34

29. cos(x)=0.55

30. sin(x)=0.28

31. cos(x)=0.71

32. cos(x)=0.07

Find the first two positive solutions.

33. 7sin(6x)=2

34. 7sin(5x)=6

35. 5cos(3x)=3

36. 3cos(4x)=2

37. 3sin(π4x)=2

38. 7sin(π5x)=6

39. 5cos(π3x)=1

40. 3cos(π2x)=2

Answer

1. 5π4, 7π4

3. π3, 5π3

5. π2

7. π2, 3π2

9. π4+2πk, 7π4+2πk, where k is an integer

11. 7π6+2πk, 11π6+2πk, where k is an integer

13. π18+2π3k, 5π18+2π3k, where k is an integer

15. 5π12+2π3k, 7π12+2π3k, where k is an integer

17. π6+πk, 5π6+πk, where k is an integer

19. π4+2π3k, 5π12+2π3k, where k is an integer

21. 4+8k, where k is an integer

23. 16+2k, 56+2k, where k is an integer

25. 0.2734, 2.8682

27. 3.7603, 5.6645

29. 2.1532, 4.1300

31. 0.7813, 5.5019

33. 0.04829, 0.47531

35. 0.7381, 1.3563

37. 0.9291, 3.0709

39. 1.3077, 4.6923


This page titled 7.4E: Solving Trigonometric Equations (Exercises) is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by David Lippman & Melonie Rasmussen (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform.

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