SOLUTION: find the exact solutions of cos theta if sin theta = 3/4 pi/2 is less than or equal to theta and theta is less than or equal to pi

Question 1158058: find the exact solutions of cos theta if sin theta = 3/4 pi/2 is less than or equal to theta and theta is less than or equal to pi

Found 3 solutions by Theo, Boreal, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
sin theta = 3/4 * pi/2 = 1.178097245.
sine can't be greater than 1, so there is something wrong with your problem th way it's written, as far as i can tell.

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
This is in the second quadrant
sin is positive and cos is negative
the triangle is x/3/4
so x^2+9=16
third side is sqrt (7)
so cosine (x)= -sqrt(7)/4

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

I think the other tutor misinterpreted the question because it was presented poorly.

I think the problem is to find cos(theta) if sin(theta) = 3/4 AND theta is between pi/2 and pi.

theta between pi/2 and pi means 2nd quadrant, where cosine is negative.

Then sin^2+cos^2=1 gives us |cos(theta)| = sqrt(7)/4; and since cosine is negative in quadrant II....

ANSWER: cos(theta) = -sqrt(7)/4

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