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Answer 1 · 2017-08-23T18:42:29

#-1#

We can add multiples of #2pi# to #(-5pi)/2# to find coterminal angles.

#(-5pi)/2+2pi=-pi/2#

This is located on the #y#-axis between Quadrant #"III"# and Quadrant #"IV"#.

The point on the unit circle at this location is #(0,-1)#, so

#sin((-5pi)/2)=sin(-pi/2)=-1#

Answer 2 · 2017-08-23T18:47:34

-1

sin#(-5 pi)/2#= - sin #(5pi)/2#

= -sin #(2pi + pi/2)#

= - sin #pi/2# = -1