SOLUTION: Use double-angle identities to find values of the sine and cosine functions for each angle measure. Find sin theta and cos theta given cos 2 theta = 5/13 and 0 < theta

SOLUTION: Use double-angle identities to find values of the sine and cosine functions for each angle measure. Find sin theta and cos theta given cos 2 theta = 5/13 and 0 < theta < pi/2

Question 546902: Use double-angle identities to find values of the sine and cosine functions for each angle measure.
Find sin theta and cos theta given cos 2 theta = 5/13 and 0 < theta < pi/2
cos theta:
sin theta:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use double-angle identities to find values of the sine and cosine functions for each angle measure. Find sin theta and cos theta given cos 2 theta = 5/13 and 0 < theta < pi/2
cos theta:
sin theta:
..
use x in place of theta
Use half-angle formulas:
cos(2x)=5/13
cos(x)=cos(2x/2)=√[(1+cos(2x))/2]=√[(1+5/13)/2]=√[(18/13)/2]
=√[(18/26]=√(9/13)=3/√13
cos(x)=(3/√13)
..
sin(2x)=12/13 (by pythagorean theorem)
sin(x)=sin(2x/2)=√[(1-cos(2x))/2]=√[(1-5/13)/2]=√[(8/13)/2]
=√[(8/26]=√(8/26)=√(4/13)
sin(x)=√(4/13)
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