Use the x y coordinates in the figure to find the value of t

Use the (x, y) coordinates in the figure to find the value of the trigonometric function at the indicated real number t, or state that the expression is undefined. csc pi/2 Select the correct choice below and if necessary, fill in the answer box to complete your choice csc pi/2 = The expression is undefined.

Solution

At pi/6 : ( sqrt3/2 , 1)

At pi/3 : ( 1/2 , sqrt3/2)

cscpi/2 = 1/sinpi/2

sin(pi/2) = sin(pi/3 +pi/6)

= sinpi/3cospi/6 + cospi/3sinpi/6

= (sqrt(3)/2)*sqrt(3)/2 +(1/2)(1/2

= (3 +1)/4

=1

cscpi/2 = 1