SOLUTION: use a half angle identity to find the exact value of the expression sin 105 degrees

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Question 482089: use a half angle identity to find the exact value of the expression
sin 105 degrees
Answer by lwsshak3(11628) About Me  (Show Source):
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use a half angle identity to find the exact value of the expression
sin 105 degrees.
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sin(x/2)=±√((1-cosx)/2)
sin 105º=sin (210º/2)=±√((1-cos210º)/2)
cos 210º=cos 30º=-√3/2 (in quadrant III where cos<0)
=±√((1+√3/2)/2)
multiply by LCD 2
=±√((2+√3)/4)
take sqrt of positive root because sin 105º in quadrant II is positive
sin 105º=√(2+√3)/2