Question

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

Answer 1

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

Explanation:

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`