document.write( "Question 349082: Find the exact value of sin (theta)/2 if cos (theta) = 2/3 and 270 deg. < (theta) < 360 deg. \n" ); document.write( "

Algebra.Com's Answer #249591 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
(For reasons I do not know, Algebra.com's formula software does not do theta, So I will be using alpha, $\"alpha\"$ , instead.

\n" ); document.write( "The general formula is $\"sin%28alpha%2F2%29+=+0+%2B-+sqrt%28%281-cos%28alpha%29%29%2F2%29\"$
\n" ); document.write( "(The zero in front is due to another limitation of Algebra.com's software.)
\n" ); document.write( "Since $\"alpha\"$ is between 270 and 360, sin is negative so we will use:
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%28%281-cos%28alpha%29%29%2F2%29\"$
\n" ); document.write( "Replacing $\"cos%28alpha%29\"$ with 2/3 we get:
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%28%281-%282%2F3%29%29%2F2%29\"$
\n" ); document.write( "Simplifying:
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%28%283%2F3-%282%2F3%29%29%2F2%29\"$
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%28%281%2F3%29%2F2%29\"$
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%281%2F6%29\"$
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%28%281%2F6%29%286%2F6%29%29\"$
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%286%2F36%29\"$
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%286%29%2Fsqrt%2836%29\"$
\n" ); document.write( " $\"sin%28alpha%2F2%29+=+-+sqrt%286%29%2F6\"$
\n" ); document.write( "which is the simplified, exact value for $\"sin%28alpha%2F2%29\"$ . \n" ); document.write( "

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