How do you find the solution to $sec^2theta-7sectheta+12=0$ if $0<=theta<360$ ?

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Answer 1 · 2017-01-11T14:27:44

$x=70.53° or x=75.52° or x=289.47 or x=284.48°$

You would use the quadratic formula to solve $secx$

$secx=(7+-sqrt(49-48))/2=(7+-1)/2$

$secx=3 or secx=4$

Since

$secx=1/cosx$

you would solve:

$1/cosx=3 or 1/cosx=4$

that's

$cosx=1/3 or cosx=1/4$

$x=arccos(1/3) or x=360-arccos(1/3) or x=arccos(1/4) or x=360-arccos(1/4)$

$x=70.53° or x=75.52° or x=289.47 or x=284.48°$

How do you find the solution to sec^2theta-7sectheta+12=0sec^2theta-7sectheta+12=0 if 0<=theta<3600<=theta<360?