document.write( "Question 840719: Use the sum or difference identities to find the exact value of sin -165 degrees \n" ); document.write( "
Algebra.Com's Answer #506666 by lwsshak3(11628)\"\" \"About 
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Use the sum or difference identities to find the exact value of sin -165 degrees
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\n" ); document.write( "Identity: sin(x-y)=sinxcosy-cosxsiny
\n" ); document.write( "sin(-165˚)=sin(60-225)=sin(60)cos(225)-cos(60)sin(225)
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\n" ); document.write( "sin(60)=√3/2
\n" ); document.write( "sin(225)=-√2/2(ref angle of π/4 in quadrant III)
\n" ); document.write( "cos(60)=1/2
\n" ); document.write( "cos(225)=-√2/2(ref angle of π/4 in quadrant III)
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\n" ); document.write( "sin(-165˚)=√3/2*-√2/2-1/2*-√2/2=√6/4-√2/4=(√6-√2)/4
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\n" ); document.write( "Calculator check:
\n" ); document.write( "sin(-165˚)=-sin(π/4)≈-0.2588
\n" ); document.write( "exact value as calculated: (√6-√2)/4≈-0.2588 \n" ); document.write( "
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