SECTION 71 The Inverse Sine Cosine and Tangent Func 451 nd t

SECTION 7.1 The Inverse Sine Cosine and Tangent Func 451 nd the exact value of each expression. Do not use a calculator sioms 57, 4s Jind the evay 38. sin- sin 38. sin-l sin (- 42. cos-11 cos(- 10 39. tan, tan(- 3m 40. sin sin 44. tan- tan \\43, tan-1( tanm 5s-$2, find the exact value, if any, of each composite function. If there is no value, say i is not defined D e, say it is \"not defined Do not use 48, tan(tan(-2)] 52. sin sin(-1.5)] 46. cos cos--21 46. co-(cos-1(-)] sin 47 47. tan (tan 14) tan ( tan 4 50. sinfsin(-2) 51. tan (tan) 33-60,find the inverse function f of each function f Find the range of f and the domain and range of f \", Problems 53-60, find the inverse 5 f(x)--2 cos (3x): O sKS 56. f(x) = 3 sin(2x);-:-x 58. f(x) cos(x + 2) +1: -2s ST-2 58. f) -cos+2)+1:-25x5-2 60,f(x) (3r + 2)-2sxs--+ =2cos Problents 61-68, find the exact solution of each equation 62, 2 cos-1x = 63.3 cos-1(2x) = 2 65, 3 tan-1x- 66-4 tan-1x = 6-6 sin-1(3r) = 68. 5 sin- 2m 2 sinx 3m Applications and Extensions Problens 69-74, use the following discu ms 69-74, use the following discussion. The formula cos-I (tan i tan ) I Pola Pole Sun 0 North latitude D 241 an be used keed to approximate the number of hours of daylight Equator or any date between the vernal equinox and autumnal l fiund as the angle i mie declination ofthe Sun is iat a location , north

Solution

41)

sin^-1(sin(9_/8))

=sin^-1(sin(+(_/8)))

=sin^-1(-sin(_/8))

=-sin^-1(sin(_/8))

=-(_/8)

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42)

cos^-1[cos(-5_/3)]

=cos^-1[cos(2-(5_/3))]

=cos^-1[cos(_/3)]

=(_/3)

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43)

tan^-1[tan(4_/5)]

=tan^-1[tan(-(_/5))]

=tan^-1[-tan(_/5)]

=-tan^-1[tan(_/5)]

=-(_/5)

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44)

tan^-1[tan(-2_/3)]

=tan^-1[-tan(2_/3)]

=tan^-1[-tan(-(_/3))]

=tan^-1[-(-tan(_/3))]

=tan^-1[tan(_/3)]

=(_/3)