How do you find the solution to $8costheta=3-4costheta$ if $0<=theta<360$ ?

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Answer 1 · 2018-07-05T22:08:02

$x=75.522^\circ, 284.477^\circ$

Given that

$8\cos\theta=3-4\cos\theta$

$8\cos\theta+4\cos\theta=3$

$\cos\theta=3/12$

$\cos\theta=1/4$

$\theta=2n\pi\pm \cos^{-1}(1/4)$

Where, $n$ is any integer i.e. $n=0, \pm1, \pm2, \pm3, \ldots$

But given that $0\le \theta<360^\circ$ hence setting $n=0$ & $n=1$ & taking positive & negative signs respectively we get

$\theta=\cos^{-1}(1/4), 2\pi-\cos^{-1}(1/4)$

$x=75.522^\circ, 284.477^\circ$

How do you find the solution to 8costheta=3-4costheta8costheta=3-4costheta if 0<=theta<3600<=theta<360?