Use the figure to find the exact value of the following trig

Use the figure to find the exact value of the following trigonometric function. cos alpha/2 cos alpha/2 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

Hypotenuse=sqrt(64+36)=10

cos alpha= adjacent/hypotenuse= 8/10=4/5

cos(alpha/2)=sqrt(1+cos alpha)/2

                    = sqrt(1+4/5)/2

                    =sqrt(9/10)=3/sqrt 10