Question

Suppose `tantheta=1/4` and theta is in the third quadrant, what are the 5 other trig function values of theta?

Answer 1

`tan t = 1/4`. t lies in Quadrant 3.
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 +1/16) = 16/17`
`cos t = - 4/sqrt17` (because t is in Quadrant 3)
`sin^2 t = 1 - cos^2 t = 1 - 16/17 = 1/17`
`sin t = - 1/sqrt17` (because t lies in Q. 3)
`tan t = 1/4`
`cot t = 4`
`sec t = 1/cos = - sqrt17/4`
`csc t = - sqrt 17`