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#