SOLUTION: If theta is an acute angle with cos theta=2/sqr rt 5, find the exact value of cos2 theta.
My possible answers are:
-3/5
-2/5
2/5
3/5
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-> SOLUTION: If theta is an acute angle with cos theta=2/sqr rt 5, find the exact value of cos2 theta.
My possible answers are:
-3/5
-2/5
2/5
3/5
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Question 69282: If theta is an acute angle with cos theta=2/sqr rt 5, find the exact value of cos2 theta.
My possible answers are:
-3/5
-2/5
2/5
3/5 Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! If theta is an acute angle with cos theta=2/sqr rt 5, find the exact value of cos2 theta.
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cos(2x)=cos^2x-sin^2x
You are given cosx=2/sqrt5
Draw a right triangle with hyp=sqrt5 and side adjacent to angle x being 2
Solve for the 3rd side which is sqrt((sqrt5)^2-2^2) = 1
Then you have sin(x) = 1/sqrt5.
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So cos(2theta) = cos^2(theta) - sin^2(theta)
=(2/sqrt5)^2 - (1/sqrt5)^2
=4/5 - 1/5
= 3/5
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Cheers,
Stan H.
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