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How do you evaluate sin(-3π/2)?

Answer 1

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

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#

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Answer 2

Emery Adkins

sin(-3π/2) = -1

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.