Question

Cos(x-30°)=0
how???????????????

Answer 1

x = n*360° + 120° or x = n*360° + 300°

Explanation:

cos(x-30°)=0

x-30° = 90° or x-30° = 270°

it means can be : x-30° = n*360° + 90° or x-30° =n*360° + 270°

x = n*360° + 120° or x = n*360° + 300° n is integers

Answer 2

Explanation:

I'm assuming you're trying to solve this for x. We use the difference identity for cosine and rewrite:

`cos(x-30)=cosxcos30+sinxsin30` and simplify using the unit circle to help.

`cosx((√(3) )/(2))+sinx((1)/(2))=0\\cosx((√(3) )/(2))=-(1)/(2) sinx\\cosx=-(1)/(2)((2)/(√(3) ))sinx\\cosx=-(1)/(√(3) )sinx\\1=-(1)/(√(3) )(sinx)/(cosx)\\1=-(1)/(√(3) )tanx\\-√(3) =tanx`

and on the unit circle, the angle where the tangent is negative square root of 3 is -60° which is also a positive 300°