SOLUTION: Find the complete solution of the equation {{{cos(x)sin^2(x)-(3cos(x))/4 = 0}}} in radians. Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: Find the complete solution of the equation {{{cos(x)sin^2(x)-(3cos(x))/4 = 0}}} in radians. Thanks!      Log On


   

Question 1083033: Find the complete solution of the equation cos%28x%29sin%5E2%28x%29-%283cos%28x%29%29%2F4+=+0 in radians.
Thanks!
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28x%29sin%5E2%28x%29-%283cos%28x%29%29%2F4+=+0

Multiply through by 4 to clear the fraction:

4cos(x)sinē(x)-3cos(x) = 0

Factor out cos(x)

cos(x)[4sinē(x)-3] = 0

cos(x)=0;    4sinē(x)-3 = 0
x = %282n%2B1%29%2Api%2F2;   4sinē(x) = 3
                     sinē(x) = 3%2F4
                      sin(x) = %22%22+%2B-+sqrt%283%29%2F2
                           x = matrix%281%2C3%2Cpi%2F3%2Bn%2Api%2C%22%2C%22%2C2pi%2F3%2Bn%2Api%29

for any integer n, positive, negative, or 0.

Edwin

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


















or



John

My calculator said it, I believe it, that settles it