How do you evaluate #sin((3pi)/2) #?

1 Answer
Alan P.
Jul 30, 2015

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

Explanation:

In standard position, an angle of #(3pi)/2# has a hypotenuse which falls along the negative Y-axis.

If a hypotenuse of unit length is swung towards the negative Y-axis, the side opposite the origin approaches -1.
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Since #sin(theta)# is defined as the ratio of the opposite side to the hypotenuse,
as #theta rarr (3pi)/2#
#color(white)("XXXXXXXX")##sin(theta) rarr -1/1#

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