document.write( "Question 927049: find cos(s+t) given that sin s=-1/2, with s in quadrant IV, and sin t=1/4 in quadrant II \n" ); document.write( "

Algebra.Com's Answer #562657 by lwsshak3(11628) $\"\"$ $\"About$

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find cos(s+t) given that sin s=-1/2, with s in quadrant IV, and sin t=1/4 in quadrant II
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\n" ); document.write( "sin s=-1/2
\n" ); document.write( "s=11π/6
\n" ); document.write( "cos s=√3/2
\n" ); document.write( "sin t=1/4
\n" ); document.write( "cos t=-√(1-sin^2(t))=-√(1-1/16)=-√(15/16)=-√15/4
\n" ); document.write( "..
\n" ); document.write( "cos(s+t)=cos s*cos t-sin s*sin t=√3/2*-√15/4--1/2*1/4=-√45/8+1/8=(-√45+1)/8
\n" ); document.write( "check:
\n" ); document.write( "s=11π/6=330˚
\n" ); document.write( "sin t=1/4
\n" ); document.write( "t≈165.52˚
\n" ); document.write( "s+t=495.52
\n" ); document.write( "cos(s+t)≈cos(495.52˚)≈-0.7135
\n" ); document.write( "exact value as computed=(-√45+1)/8≈0.7135 \n" ); document.write( "

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