document.write( "Question 546902: Use double-angle identities to find values of the sine and cosine functions for each angle measure.\r
\n" ); document.write( "\n" ); document.write( "Find sin theta and cos theta given cos 2 theta = 5/13 and 0 < theta < pi/2\r
\n" ); document.write( "\n" ); document.write( "cos theta:
\n" ); document.write( "sin theta: \n" ); document.write( "

Algebra.Com's Answer #356203 by lwsshak3(11628) $\"\"$ $\"About$

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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
\n" ); document.write( "cos theta:
\n" ); document.write( "sin theta:
\n" ); document.write( "..
\n" ); document.write( "use x in place of theta
\n" ); document.write( "Use half-angle formulas:
\n" ); document.write( "cos(2x)=5/13
\n" ); document.write( "cos(x)=cos(2x/2)=√[(1+cos(2x))/2]=√[(1+5/13)/2]=√[(18/13)/2]
\n" ); document.write( "=√[(18/26]=√(9/13)=3/√13
\n" ); document.write( "cos(x)=(3/√13)
\n" ); document.write( "..
\n" ); document.write( "sin(2x)=12/13 (by pythagorean theorem)
\n" ); document.write( "sin(x)=sin(2x/2)=√[(1-cos(2x))/2]=√[(1-5/13)/2]=√[(8/13)/2]
\n" ); document.write( "=√[(8/26]=√(8/26)=√(4/13)
\n" ); document.write( "sin(x)=√(4/13) \n" ); document.write( "

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