document.write( "Question 818300: I was given the following problem but I am having difficulty with it: \r
\n" ); document.write( "\n" ); document.write( "compute the exact values of sin x/2, cos x/2, tan x/2
\n" ); document.write( "tan x=3/4, -pi\n" ); document.write( "\n" ); document.write( "Can you show me the process of how to solve this?
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Algebra.Com's Answer #492554 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
I was given the following problem but I am having difficulty with it:
\n" ); document.write( "compute the exact values of sin x/2, cos x/2, tan x/2
\n" ); document.write( "tan x=3/4, -pi
\n" ); document.write( "***
\n" ); document.write( "Identities:
\n" ); document.write( " $\"sin%28x%2F2%29=sqrt%28%281-cos%28x%29%29%2F2%29\"$
\n" ); document.write( " $\"cos%28x%2F2%29=sqrt%28%281%2Bcos%28x%29%29%2F2%29\"$
\n" ); document.write( " $\"tan%28x%2F2%29=sin%28x%29%2F%281%2Bcos%28x%29%29\"$
\n" ); document.write( "..
\n" ); document.write( "Assume reference angle x is quadrant I
\n" ); document.write( "You are working with a 3-4-5 right triangle in quadrant I
\n" ); document.write( "sin(x)=3/5
\n" ); document.write( "cos(x)=4/5
\n" ); document.write( "..
\n" ); document.write( " $\"sin%28x%2F2%29=sqrt%28%281-%284%2F5%29%29%2F2%29=sqrt%28%281%2F5%29%2F2%29\"$ =1/√10=√10/10
\n" ); document.write( " $\"cos%28x%2F2%29=sqrt%28%281%2Bcos%28x%29%29%2F2%29=sqrt%28%281%2B%284%2F5%29%29%2F2%29\"$ =√(9/10)=3/√10=3√10/10
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\n" ); document.write( "..
\n" ); document.write( "calculator check:
\n" ); document.write( "tan(x)=3/4
\n" ); document.write( "x≈36.8698˚
\n" ); document.write( "x/2≈18.4349˚
\n" ); document.write( "..
\n" ); document.write( "sin(x/2)≈sin(18.4349)≈0.3162..
\n" ); document.write( "exact value as calculated=√10/10≈0.3162..
\n" ); document.write( "..
\n" ); document.write( "cos(x/2)≈cos(18.4349)≈0.9486..
\n" ); document.write( "exact value as calculated=3√10/10≈0.9486..
\n" ); document.write( "..
\n" ); document.write( "tan(x/2)=tan(18.4349)≈0.3333..
\n" ); document.write( "exact value as calculated=1/3\r
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