APPENDIX D TRIGONOMETRY A33 56. tan x + tan y sin(x + y) COS X Cos y position, as in the figure. Express x and y in terms of 0 and then use the distance formula to compute c.] 57, sin 30+ sin 0 = 2 sin 20 cos 0 and sau amuz giliw to YEW In 58. cos 30 = 4 cos0 - 3 cos 0 (a) mottaton Emg84. In order to find the distance |AB| across a smail inlet, a point C was located as in the figure and the following measurements 59-64 If sin x = and sec y =, where x and y lie between 0 and /2, evaluate the expression. 59. sin(x + y) were recorded: trollinite LC = 103 01901 | AC = 820 m | BC = 910 m 61. cos(x - y) 63. sin 2y 60. cos(x + y) 62. sin(x - y) 64. cos 2y 65-72 Find all values of x in the interval [0, 27] that satisfy the equation. 65. 2 cos x1 = 0 67. 2 sinx = 1 69. sin 2x = cos x) *19119 71. sin x = tan x 66. 3 cot2x = 1 68. | tan x = 1 70. 2 cos x + sin 2x = 0 2916oibni 72. 2+ cos 2x = 3 cos x 73-76 Find all values of x in the interval [0, 2] that satisfy the inequality. 73. sin x ] (moitamme A B 1985. Use the figure to prove the subtraction formula cos(a-B) = cos a cos + sin a sin [Hint: Compute c in two ways (using the Law of Cosines from Exercise 83 and also using the distance formula) and compare the two expressions.] C B(cos , sin ) YA sitive A (cos a, sin a) 1 1 7 roved by that aB 0 ema TRO e76) or by the 1855) 86. Use the formula in Exercise 85 to prove the addition formula for cosine (12b). 87. Use the addition formula for cosine and the identities tically, we supinu on a s T COS - 2 = sin MOLT/102 2 sin (7-0) - = cos 0 to prove the subtraction formula (13a) for the sine function. 88. Show that the area of a triangle with sides of lengths a and b and with included angle is b C A = = ab sin 0 H (a, 0) [Hint: Introduce a coordinate system so that is in standard 89. Find the area of triangle ABC, correct to five decimal places, if |AB|= 10 cm | BC|= 3 cm LABC=107