Determine the quadrant in which the angle lies and state its

Determine the quadrant in which the angle lies and state its reference angle. In addition, find an angle between 0 and 2 pi radians, or 0 degree and 360 degree, that is coterminal with the given angle. Finally, determine the value of the given trigonometric function. 17 pi/3 Quadrant: _____ Quadrant: _____ Ref angle: _____ Ref angle: _____ degrees Coterminal angle: _____degrees Co terminal angle _____ degrees Calculate exactly: sin(17 pi/3) = Calculate exactly: sec(-870 degree) =

Solution

a. 17pi/3

   6pi - pi/3 lies in fourth quadrant

reference angle

To find the reference angle we have to subtract it from 6pi

and 6pi - 17pi/3=pi/3

reference angle=pi/3

Coterminal angle

To find the coterminal angle we have to subtract 4pi from it

17pi/3 - 4pi=5pi/3 and that\'s the coterminal angle

sin(17pi/3)=sin(6pi - pi/3)= -sqrt3/2