If cos 2x = sion x, and x is in radians, radians, which of the following is a possible value of x ?

Options

A. `0.39`
B. `0.52`
C. `1.05`
D. `1.60`

Answer

B

Explanation

Use the relationship cos `2x=1-2 sin^(2)` x to get everything in terms of sine. And be sure your calculator is in radian mode.
`cos 2x = sin x`
`1-2 sin^(2)x = sin x`
`2sin^(2)x + sin x - 1 =0`
`(2 sin x-1)(sin x + 1)=0`
`sin x = (1)/(2)` or `-1`
x = arcsin `((1)/(2))` or arcsin `(-1)`
`~~0.52` or `-1.57`
Of those solutions, only `0.52` is listed in the answer choices.