document.write( "Question 498900: Use a sum or difference formula to determine the value of the trigonometric function.\r
\n" ); document.write( "\n" ); document.write( "cos(7π/4+5π/6)\r
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Algebra.Com's Answer #337424 by lwsshak3(11628) $\"\"$ $\"About$

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Use a sum or difference formula to determine the value of the trigonometric function.
\n" ); document.write( "cos(7π/4+5π/6)
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\n" ); document.write( "cos(s+t)=cos s cos t - sin s sin t
\n" ); document.write( "For given function:
\n" ); document.write( "s=7π/4
\n" ); document.write( "t=5π/6
\n" ); document.write( "..
\n" ); document.write( "Cos s=cos(7π/4)=cos π/4 in quadrant IV=√2/2
\n" ); document.write( "Cos t=cos(5π/6)=cos π/6 in quadrant II=-√3/2
\n" ); document.write( "..
\n" ); document.write( "sin s=sin(7π/4)=sin π/4 in quadrant IV=-√2/2
\n" ); document.write( "sin t=sin(5π/6)=sin π/6 in quadrant II=1/2
\n" ); document.write( "..
\n" ); document.write( "cos(7π/4+5π/6)
\n" ); document.write( "=(√2/2*-√3/2)-(-√2/2*1/2)
\n" ); document.write( "=-√6/4-(-√2/4)
\n" ); document.write( "=(-√6+√2)/4
\n" ); document.write( "Check:
\n" ); document.write( "cos(7π/4+5π/6)=cos(315+150)=cos 465º=-.2588
\n" ); document.write( "(-√6+√2)/4=-.2588 \n" ); document.write( "

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