How do you evaluate sin(-3π/2)?

1 Answer
Dec 17, 2015

#sin(-(3pi)/2) = 1#

Explanation:

As an angle #-(3pi)/2# is equivalent to #pi/2#

#-(3pi)/2# is #3/4# of a circle in a clockwise direction.
#pi/2# is #1/4# of a circle in a counter clockwise direction.

#sin(pi/2) =1#

If you think in terms of a unit radius circular segment centered on the origin of the Cartesian plane with its base along the positive X-axis, then the inscribed right-angled triangle at #pi/2# will have a vertex on the positive Y-axis and both the hypotenuse and opposite side will have a length of #1#