SOLUTION: Solve the equation for 0≤x≤{{{2pi}}}. Write your answer as a multiple of {{{pi}}}. cos(x)= cos{{{(pi/2)- (x)}}} Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation for 0≤x≤{{{2pi}}}. Write your answer as a multiple of {{{pi}}}. cos(x)= cos{{{(pi/2)- (x)}}} Thanks!       Log On


   

Question 1083045: Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi.
cos(x)= cos%28pi%2F2%29-+%28x%29

Thanks!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%29=cos%28pi%2F2-x%29 is a commonly remembered trigonometric identity.
Substituting sin%28x%29 for cos%28pi%2F2-x%29 in the equation given,
you get cos%28x%29=sin%28x%29 .
cos%28theta%29 and sin%28theta%29 are the x- and y-coordinates of the point P%28x%2Cy%29
on the unit circle that you reach when you move along the circle counterclockwise
a distance theta from point A%281%2C0%29 .
The points with x=y are on the diagonal bisecting quadrants I and III,
so there are only two angles with cos%28x%29=sin%28x%29 between 0 and 2pi :
highlight%28pi%2F4%29 and highlight%285pi%2F4%29 .