document.write( "Question 694532: I don't know how to find the exact value of cos 23pi/12 using the properties of special triangles \n" ); document.write( "

Algebra.Com's Answer #428052 by lwsshak3(11628) $\"\"$ $\"About$

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find the exact value of cos 23pi/12 using the properties of special triangles
\n" ); document.write( "Use cos half-angle identity
\n" ); document.write( "cos(x/2)=ą√[(1+cos(x)/2]
\n" ); document.write( "cos(23π/12)=cos(23π/6)/2)=√[(1+cos(23π/6)/2]
\n" ); document.write( "For cos(23π/6) use reference angle π/6 in quadrant IV where cos>0
\n" ); document.write( "cos(23π/6)=cos(π/6)=√3/2
\n" ); document.write( "cos(23π/12)
\n" ); document.write( "=cos(23π/6)/2)
\n" ); document.write( "=√[(1+cos(23π/6)/2]
\n" ); document.write( "=√[(1+√3/2/2]
\n" ); document.write( "calculator check:
\n" ); document.write( "cos(23π/12)≈0.9659..
\n" ); document.write( "√[(1+√3/2/2]≈0.9659.. \n" ); document.write( "

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