How do you find the general solutions for 5cos(x) + 4= Sec(x)5cos(x)+4=sec(x)?

1 Answer
Nghi N.
Aug 12, 2015

Solve: 5cos X + 4 = sec x

Explanation:

5cos x + 4 = 1/cos x5cosx+4=1cosx
5cos^2 x + 4cos x - 1 = 0.5cos2x+4cosx−1=0.
Since a - b + c = 0, use the shortcut. The 2 real roots are:
cos x = - 1, and cos x = -c/a = 1/5cosx=−ca=15

a. cos x = -1 --> x = pi + kpix=π+kπ

b. cos x = 1/5 = 0.20 --> x = +- 78.46 deg + 2k(360)x=±78.46deg+2k(360)

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