How do you find the exact value of $cos^3x-3/4cosx=0$ in the interval $0<=x<360$ ?

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Answer 1 · 2017-01-31T04:55:16

$30^o , 90^o, 150^o, 210^o, 270^o and 330^o$

Here, $cos 3x = 4cos^x-3cos x = 0 = cos(pi/2)$ ,

with the general solution,

$3x = 2kpi+-pi/2, k = 0, +-1, +-2, +-3, ...,$ giving

$x=(120k+-30)^o, k = 0, +-1, +-2, +-3, ...$

In $[0, 360^o]$

$x=30^o , 90^o, 150^o, 210^o, 270^o and 330^o$

How do you find the exact value of cos^3x-3/4cosx=0cos^3x-3/4cosx=0 in the interval 0<=x<3600<=x<360?