Question #72dcf

1 Answer
Nghi N
May 18, 2017

#x = 74^@14 + k360^@#
#x = - 51^@52 + k360^@#

Explanation:

cos x + (0.2)sin x = 0.466
Call t the arc that tan t = 0.20 --> # t = 11^@31 #--> cos t = 0.98
#cos x + ((sin t)/(cos t))sin x = 0.466#
#cos x.cos t + sin t.cos x = (0.466)cos t = (0.466)(0.98) = 0.457#
Use trig identity:
cos (x - t) = cos x.cos t - sin t.sin x
In this case:
#cos (x - 11.31) = 0.457 = cos 62^@83#
#x - 11.31 = +- 62.83#

a. #x - 11.31 = 62.83# --> #x = 63.83 + 11/31 = 74^@14#
b. x - 11.31 = - 62.83
#x = 11.31 - 62.83 = - 51^@52#
General answers:
#x = 74^@14 + k360^@#
#x = -51^@52 + k360^@#

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