Question

Cos(x-30°)=0 how???????????????

Answer 1

Answer:

Step-by-step 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.

$cosx(\frac{\sqrt{3} }{2})+sinx(\frac{1}{2})=0\\cosx(\frac{\sqrt{3} }{2})=-\frac{1}{2} sinx\\cosx=-\frac{1}{2}(\frac{2}{\sqrt{3} })sinx\\cosx=-\frac{1}{\sqrt{3} }sinx\\1=-\frac{1}{\sqrt{3} }\frac{sinx}{cosx}\\1=-\frac{1}{\sqrt{3} }tanx\\-\sqrt{3} =tanx$

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

Answer 2

Answer:

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

Step-by-step 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