document.write( "Question 677446: exact value of sin 157.5 without using a calculator \n" ); document.write( "
Algebra.Com's Answer #420941 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
exact value of sin 157.5 without using a calculator
\n" ); document.write( "sin(157.5)=sin(315/2)
\n" ); document.write( "Identity: sin(x/2)=±√[(1-cosx)/2]
\n" ); document.write( "select positive identity since 175 is in the 2nd quadrant where sin>0
\n" ); document.write( "sin(315/2)=√[(1-cos315)/2]
\n" ); document.write( "cos 315=cos45 in quadrant IV=√2/2
\n" ); document.write( "sin(315/2)=√[(1-√2/2)/2]=√[(2-√2)/4]=√(2-√2)/2
\n" ); document.write( "sin(157.5)=√(2-√2)/2
\n" ); document.write( "check using calculator:
\n" ); document.write( "sin157.5º≈0.382...
\n" ); document.write( "√(2-√2)/2≈0.382... \n" ); document.write( "
\n" );