SOLUTION: Hi, I'm not sure how to go about this question : sin x + ((3)^1/2)cos x = 0 (In relation to exact value) Thankyou

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, I'm not sure how to go about this question : sin x + ((3)^1/2)cos x = 0 (In relation to exact value) Thankyou      Log On


   

Question 752819: Hi, I'm not sure how to go about this question : sin x + ((3)^1/2)cos x = 0
(In relation to exact value)
Thankyou
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%29%2Bsqrt%283%29cos%28x%29=0 --> sin%28x%29=-sqrt%283%29cos%28x%29 --> sin%28x%29%2Fcos%28x%29=-sqrt%283%29 --> tan%28x%29=-sqrt%283%29
We know that tan%2860%5Eo%29=sqrt%283%29
So tan%28-60%5Eo%29=-sqrt%283%29 because tan%28-A%29=-tan%28A%29
and also tan%28180%5Eo-60%5Eo%29=tan%28120%5Eo%29=-sqrt%283%29 because tan%28A%2B180%5Eo%29=tan%28A%29
So highlight%28x=-60%5Eo%29 and highlight%28x=120%5Eo%29 are two solutions,
and in general
highlight%28x=k%2A180%5Eo-60%5Eo%29 for all integer values of k represents all the solutions.

If you need to measure angles in radians, it would be
highlight%28x=k%2Api-pi%2F3%29