How do you find the exact value of sin7.5?

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Answer 1 · 2015-05-16T07:02:01

Use some half angle formulas:

#sin(theta/2) = +-sqrt((1-cos theta) / 2)#

#cos(theta/2) = +-sqrt((1+cos theta) / 2)#

Also use a known value #cos 30^o = sqrt(3)/2#

If we stick to the first quadrant, we can take the sign of the square root to be #+# in both cases.

#cos 15^o = sqrt((1+cos 30^o)/2)#

#= sqrt((1+sqrt(3)/2)/2)#

#= sqrt((2+sqrt(3))/4)#

#= sqrt(2+sqrt(3))/2#

#sin 7.5^o = sqrt((1-cos 15^o)/2)#

#= sqrt((1-sqrt(2+sqrt(3))/2)/2)#

#= sqrt((2-sqrt(2+sqrt(3)))/4)#

#= sqrt(2-sqrt(2+sqrt(3)))/2#