Question

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)?

Answer 1

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`