Half Angle Formulas

Half Angle Formulas

Cos x/2 = +/- √((1+cosx)/2)                          Sin x/2=+/-√((1-cos x)/2)

1.       Find the exact value of 3π/8

The first thing you do is figure out the quadrant that 3π/8 is in.  That quadrant is the first quadrant because it is 67.5˚.  So we know that cos is positive in quadrant I. 

3π/8=(1/2)(3π/4)

Using the half angle formula with x=3π/4

Cos  3π/8=+√(1+cos(3π/4)/2)

 =+√((1-√2/2)/2)

=√(2-√2)/2

2.       Simplify  √[1-cos 80˚)/2}\]

First you have to recognize this as the half angle formula for sin because of the negative in the square root.

So you half that angle and get 40˚

So the answer is sin 40˚.

Jenna Roussel