How does one find the exact values of sec, tan, and sin given the angle is in standard position whose terminal sides intersect at (-12/37, -35/37)?

1 Answer
Nghi N.
Jun 27, 2018

The point (x = -12/37, - 35/37) of the terminal side of angle t, lies in Quadrant 3.
#tan t = y/x = (-35/37)(-37/12) = 35/12#
#cos^2 t = 1/(1 +tan^2 t) = 1/(1 + 1225/144) = 144/1369#
#cos t = - 12/37# (because t lies in Quadrant 3)
#sin^2 t = 1 - cos^2 t = 1 - 144/1369 = 1225/1369#
#sin t = - 35/37# (because t lies in Quadrant 3.
#cot t = 1/(tan) = 12/35#
#sec t = 1/(cos) = - 37/12#
#csc t = 1/(sin) = - 37/35#

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