Reformatted question: Find exact value of cos(-(11pi)/2)
First, we can find a coterminal angle in the interval (-2pi,2pi) by finding the remainder when (11pi)/2 is divided by 2pi which is the angle in radians of one circle (disregard the negative sign for now, we'll add it back on after we divide):
(5.5pi)/(2pi)=(2)(2pi)+1.5pi
Therefore the remainder is 1.5pi or (3pi)/2.
Now, we know a coterminal angle of (-11pi)/2 is -(3pi)/2 (here we add the negative sign back):
cos(-(3pi)/2)
We can write cos(-(3pi)/2) as cos(pi/2) since -(3pi)/2 and pi/2 are also coterminal because -(3pi)/2 is 3/4 around the unit circle going clockwise while pi/2 is 1/4 around the unit circle going counterclockwise:
thereforecos(-(3pi)/2)=cos(pi/2)=0 since it is one of our special unit circle trig values
