SOLUTION: Suppose there is an angle theta where pi/2 <= theta <= pi. Also, sin theta = a. Find cos theta in terms of a.

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Question 904342: Suppose there is an angle theta where pi/2 <= theta <= pi. Also, sin theta = a. Find cos theta in terms of a.
Found 2 solutions by lwsshak3, KMST:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose there is an angle theta where pi/2 <= theta <= pi. Also, sin theta = a. Find cos theta in terms of a.
use x for theta
reference angle x is in quadrant II where sin>0, cos<0
sin(x)=a
cos^2(x)+sin^2(x)=1
cos(x)=-√(1-sin^2(x))=-√(1-a^2)

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
An angle theta such that pi%2F2+%3C=+theta+%3C=+pi is in quadrant II (or its borders),
where sine is positive (or zero), and cosine is negative (or zero), so cos%28theta%29%3C=0.
We know that %28sin%28theta%29%29%5E2%2B%28cos%28theta%29%29%5E2=1 , so if sin%28theta%29+=+a ,
then a%5E2%2B%28cos%28theta%29%29%5E2=1 ---> %28cos%28theta%29%29%5E2=1-a%5E2 ,
and since cos%28theta%29%3C=0 , it must be highlight%28cos%28theta%29=-sqrt%281-a%5E2%29%29