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. 2 sin theta/2 cos theta/2 2sin theta/2 cos theta/2= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

sin2@ = 2*sin@*cos@

so sin@ = 2*sin(@/2)*cos(@/2)

so 2*sin(@/2)*cos(@/2)     = sin@

= perpendicular / hypotenuse

= 3 / 5   

[ from fig H = ( 3² + 4² )^1/2  = 5 ]