How do you use half angle formula to find sin 67.5?

1 Answer
May 4, 2018

sqrt(2+sqrt2)/2

Explanation:

sin67.5^@

The half angle formula for sin(theta/2) = +-sqrt((1-costheta)/2).

The +- sign depends on which quadrant your angle is in. Since 67.5^@ is in the 1st quadrant and sine is positive in that quadrant, we know that it is positive.

67.5^@ * 2 = 135^@, so:
sin(theta/2) = sqrt((1- cos135^@)/2)

quadquadquadquadquadquadquad=sqrt((1-(-sqrt2/2))/2)

quadquadquadquadquadquadquad=sqrt((2/2+sqrt2/2)/2)

quadquadquadquadquadquadquad=sqrt(((2+sqrt2)/2)/2)

quadquadquadquadquadquadquad=sqrt((2+sqrt2)/4)

quadquadquadquadquadquadquad=sqrt(2+sqrt2)/2

Hope this helps!