. 27. sin (30) = -1

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
Question

Number 27, please. 

# Skill Building

**In Problems 13-36, solve each equation on the interval \(0 \leq \theta < 2\pi\).**

13. \(\sin \theta = \frac{1}{2}\)

14. \(\cos \theta + 1 = 0\)

15. \(2\sin \theta + 1 = 0\)

16. \(\cos \theta + 1 = 0\)

17. \(\tan \theta - 1 = 0\)

18. \(\sqrt{3} \cot \theta + 1 = 0\)

19. \(4 \sec \theta + 6 = -2\)

20. \(5 \csc \theta - 6 = -1\)

21. \(3\sqrt{2} \cos \theta + 2 = -1\)

22. \(4 \sin \theta + 3 \sqrt{3} = \sqrt{3}\)

23. \(4 \cos^2 \theta = 2\)

24. \(\tan^2 \theta = \frac{1}{3}\)

25. \(2 \sin \theta - 1 = 0\)

26. \(4 \cos^2 \theta = 3\)

27. \(\sin \left( 3\theta \right) = -1\)

28. \(\tan \theta = \sqrt{3}\)

29. \(\cos 2\theta = 1\)

30. \(\tan \left( 2\theta \right) = -1\)

31. \(\sec 2\theta = 2\)

32. \(\cot 3\theta = 3\)

33. \(\cos \left( \frac{\theta}{3} \right) = -\frac{1}{2}\)

34. \(\sin \left( \frac{\pi}{18} \right) = 1\)

35. \(\tan \left( \frac{\theta}{2} \right) = 1\)

36. \(\cos \left( \frac{\theta}{4} \right) = \frac{\sqrt{3}}{2}\)

---

**Problems 37-46, solve each equation. Give a general formula for all the solutions. List six solutions.**

37. \
Transcribed Image Text:# Skill Building **In Problems 13-36, solve each equation on the interval \(0 \leq \theta < 2\pi\).** 13. \(\sin \theta = \frac{1}{2}\) 14. \(\cos \theta + 1 = 0\) 15. \(2\sin \theta + 1 = 0\) 16. \(\cos \theta + 1 = 0\) 17. \(\tan \theta - 1 = 0\) 18. \(\sqrt{3} \cot \theta + 1 = 0\) 19. \(4 \sec \theta + 6 = -2\) 20. \(5 \csc \theta - 6 = -1\) 21. \(3\sqrt{2} \cos \theta + 2 = -1\) 22. \(4 \sin \theta + 3 \sqrt{3} = \sqrt{3}\) 23. \(4 \cos^2 \theta = 2\) 24. \(\tan^2 \theta = \frac{1}{3}\) 25. \(2 \sin \theta - 1 = 0\) 26. \(4 \cos^2 \theta = 3\) 27. \(\sin \left( 3\theta \right) = -1\) 28. \(\tan \theta = \sqrt{3}\) 29. \(\cos 2\theta = 1\) 30. \(\tan \left( 2\theta \right) = -1\) 31. \(\sec 2\theta = 2\) 32. \(\cot 3\theta = 3\) 33. \(\cos \left( \frac{\theta}{3} \right) = -\frac{1}{2}\) 34. \(\sin \left( \frac{\pi}{18} \right) = 1\) 35. \(\tan \left( \frac{\theta}{2} \right) = 1\) 36. \(\cos \left( \frac{\theta}{4} \right) = \frac{\sqrt{3}}{2}\) --- **Problems 37-46, solve each equation. Give a general formula for all the solutions. List six solutions.** 37. \
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