Plane trigonometry with practical applications, by Leonard E. Dickson.

Ch. X]

FUNCTIONS OF SEVERAL ANGLES

149

EXERCISES ON TRIGONOMETRIC EQUATIONS
Find all the positive angles < 360~ which satisfy the following equations,
excluding angles for which any of the functions are undefined:
1. 2 sin2 x + 3 cosx = 0. 2. 16 sin2 x + 24 cos x = 9.
3. 2 cos2 x + 5 sinx = 4. 4. 2 tanx sinx = 3.
5. cosx + cos 2 x =-1. 6. cosx + secx = 5.
7. tan A + cot A = 2. 8. sin 3A = cos 2A [= sin (90~-2A)].
9. tan2y + cot2y = 2. 10. sec2 y + csc2y = 4.
11. sin 2 x = 2 sin x.
12. tan (45~ - x) + tan (45~ + x) = 4.
13. sin 4 x + cos 4 x = 1.
14. tan x + tan 2x = tan 3 x [ = tan (x + 2 x)].
15. tan x sec x = - 2. 16. sin 2 x cos x = sin x.
17. 4 tan B- cot B = 3. 18. tan B - cot B = cot 2B.
19. tan 2 0 = tan 0. 20. sc 0 - cot 0 = sin I 0.
21. 6tan 2 0- 4sin 2 0 =1. 22. csc = 1 + cot0.
By converting one or both members into a product (Art. 104), solve
23. sin 3 x + sin x = - sin 2 x.
24. sin 2 x-sinx = cos 2 x -cosx.
25. cos x - cos 3 x = sin 2 x.
26. sin x + sin 3 x = cos x - cos 3 x.
27. sin 5A + sin 3A = cos A.
28. cos 7A + cos A = - cos 5A - cos 3A.
29. sin 4A - sin 2A = cos 3A.
30. sin (A + 120~) + sin (A + 60~) = 1.5.
By the second method of Example 4, solve

31. sin x + cos x = /2.
33. 2 cos x - sinx = 1.

32. 5 sin x + 12 cos x = 6.5.
34. 5sin x + 2 cosx = 5.