How do you find the general solutions for sec(x) = - 4sec(x)=−4?

1 Answer
Nghi N.
Aug 25, 2015

x = 104^@48 + k360^@x=104∘48+k360∘
x = 255^@52 + k360^@x=255∘52+k360∘

Explanation:

cos x = 1/sec x = - 1/4 = - 0.25cosx=1secx=−14=−0.25
Calculator and unit circle give:
cos x = - 0.25cosx=−0.25 -->
x = +- 104^@48 + k360^@x=±104∘48+k360∘
Note.
x = - 104^@48x=−104∘48 is co-terminal to x = 360 - 104.48 = 255^@52x=360−104.48=255∘52

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