Question

How do you find the remaining trigonometric functions of `theta` given `cottheta-=1/2` and `costheta>0`?

Answer 1

`cot t = 1/2` --> tan t = 2
Use trig identity:
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 4) = 1/5`
`cos t = 1/sqrt5 = sqrt5/5` --> (because cos t > 0)
`sin^2 t = 1 - cos^2 t = 1 - 1/5 = 4/5`
`sin t = +- 2/sqrt5 = +- (2sqrt5)/5`
tan t = 2 , then, t is in Quadrant 1, and sin t is positive
`sin t = (2sqrt5)/5`
`sec t = 1/(cos t) = sqrt5`
`csc t = 1/(sin t) = sqrt5/2`