document.write( "Question 802182: find sin(17pie/12) \n" ); document.write( "

Algebra.Com's Answer #483788 by lwsshak3(11628) $\"\"$ $\"About$

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find exact value of sin(17pie/12)
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\n" ); document.write( "sin(17π/12)
\n" ); document.write( "=sin(8π/12+9π/12)
\n" ); document.write( "=sin(2π/3+3π/4)
\n" ); document.write( "Identity: sin(x+y)=sinxcost+cosxsiny
\n" ); document.write( "sin(2π/3+3π/4)=sin(2π/3)cos(3π/4)+cos(2π/3)sin(3π/4)
\n" ); document.write( "=√3/2*-√2/2+-1/2*√2/2=-√6/4-√2/4=-(√6+√2)/4
\n" ); document.write( "check:
\n" ); document.write( "sin(17π/12)≈-0.9659 (with calculator)
\n" ); document.write( "Exact value as calculated=-(√6+√2)/4≈0.9659 \n" ); document.write( "

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