MISCELLANEOUS EXERCISES

102. 1. An angle of 4 radians, having its vertex at the center of a circle, intercepts an arc of 7 inches; find the radius of the circle.

2π 2. Express the following in degrees: radians, radi 5

π

3

radians.

Зп ans, 4

3. Express the following in radian measure: 40°, 55°, 38°, 52° 16'.

4. Reduceradians to degrees.

5. Find the number of degrees in a central angle which intercepts an arc of 5 feet in a circle whose radius is 8 feet.

6. An arc of 12 inches subtends a central angle of 50°; find the radius of the circle.

7. The number of minutes in an angle is 71⁄2 times the number of degrees in its supplement; find the number of radians in the angle.

π

8. An angle exceeds another by radians, and their sum

8

is 160°; express each angle in radian measure.

9. The angles of a triangle are to each other as 2:3:4; express each angle in radian measure.

10. The angles of a triangle are in arithmetical progression, and the mean angle is twice the smallest; express each angle in radian measure.

11. The circumference of a circle is divided into 7 parts in arithmetical progression, the greatest part being 10 times the least; express in radians the angle which each arc subtends at the center.

12. An arc of 40° on a circle whose radius is 6 inches is equal in length to an arc of 25° on another circle; what is the radius of the latter circle?

22. sin 4 x 4 (cos3 x sin x - sin x cos x).

23. cos 4x4 cos*x + 4 sin*x 3.

25. cos 5x =

24. sin 5x =
16 cos3

16 sin x

- 20 cos3 x + 5 cos x.

26. sin (a+B+y)= sin a cos ẞ cos y

28. 2 sin (α-B) cos a = sin (2 α- ß) — sin ß.

35. cos (a+B) cos (a — ß) = cos2 α — sin2ß.

41. sin (a +ẞ) cos (a−ẞ)+cos (a+ß) sin (a− ß) = sin 2 α

= tan

2

α

2

α

[sin()+ cos()]

2

= sin a+ cos ß.

2

47. 4 sin sin (60° — 6) sin (60° + 0) = sin 3 0.

Solve each of the following equations for all values of

the unknown quantity less than 360°.

64. sin 20-2 cos 0+2 sin 0 - 2 = 0.
65. sin2 + sin 30 = 2 sin cos 20 - .
66. tan 20 cot 0 tan 20+ cot 0-1 = 0.
67. cos 70+ cos 50+ cos 30 = 0.

68. sec2 0 csc2 0 + 4 = 4 csc2 0 + sec2 0.
69. Given tan ß: =u, find sin 2 ß.

70. Given tan 0 = csc 2 0, find cos 0.

73. Given tan 2 x = m, find tan x.

74. If α+B+y=180°, show that

tana+tan ẞ+tan y = tan a tan ẞ tan y.

75. If α+B+y=180°, show that

α

cot+cot+cot = cot cot cot 2. 2 2 Y.

76. If a +ẞ+y=180°, show that

2

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