Find the exact value of each of the other five trigonometric

Find the exact value of each of the other five trigonometric functions of the angle theta given the indicated information: csc theta = squareroot 5/2 and tan theta

Solution

5. csc theta=sqrt5/2

sin theta=1/csc theta=2/sqrt5

opposite=2 , hypotenuse=sqrt5

adjacent=sqrt(5-4)=1

cos theta=adjacent/hypotenuse=-1/sqrt5

tan theta=sin theta/cos theta=-2

cot theta=1/tan theta=-1/2

sec theta=1/cos theta=-sqrt5

6 . Area of unshaded region=area of sector-area of triangle

                    = (70/360)pi *5.2²-(5.2²/2)sin 70 = 3.81315 cm²

area of shaded region =area of circle - area of unshaded region = pi 5.2²-3.81315 =81.14cm²