Use the figure and the given half angle formula to find the

Use the figure and the given half angle formula to find the exact value of cost. Assume ft* half angle lies in the first quadrant. Reduce and rationalize your final answer. Worth 8 points.

Solution

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

cos theta=adjacent/hypotenuse

adjacent=15,opposite=8

hypotenuse=sqrt(adjacent^2 + opposite^2)= 17

cos theta=15/17

cos(theta/2)=+-sqrt(1+15/17)/2 =+-4sqrt(1/17)

And in first quadrant cos theta is positive. Therefore cos (theta/2) is positive too

Therefore cos (theta/2)=4sqrt(1/17)=(4sqrt17)/17