How do you find the sine, cosine, and tangent of 19pi/2 radians?

1 Answer
Nov 5, 2015

#sin((3pi)/2) = -1#
#cos((3pi)/2) = 0#
#tan((3pi)/2) = #infinity/undefined

Explanation:

If we take away #2pi# radians from the angle, it will still be the same angle. So, we do that until it is a more recognizable angle. Since #(4pi)/2# is the same as #2pi#, we will use that.

#(19pi)/2 - (4pi)/2 - (4pi)/2 - (4pi)/2 - (4pi)/2 = (3pi)/2#
Now to find the sin, cos, and tan values of #(3pi)/2#, use the unit circle.

#sin((3pi)/2) = -1#
#cos((3pi)/2) = 0#
#tan((3pi)/2) = #infinity/undefined
https://en.wikipedia.org/wiki/Unit_circle