Question

How do you find the values of the six trigonometric functions given `cottheta=-3` and `costheta>0`?

Answer 1

Find trig function values

Explanation:

Use tri identity:
`sin^2 t = 1/(1 + cot^2 t) = 1/(1 + 9) = 1/10` -->
`sin t = +- 1/sqrt10 = +- sqrt10/10`
Since cot = - 3 < 0 and cos t > 0, there for, sin t < 0.
`sin t = - sqrt10/10`
`cos^2 t = 1 - sin^2 t = 1 - 1/10 = 9/10` -->
`cos t = 3/sqrt10 = (3sqrt10)/10`
`tan t = 1/cot t = 1/-3 = - 1/3`
`sec t = 1/(cos) = 10/(3sqrt10) = sqrt10/3`
`csc t = - 10/sqrt10 = - sqrt10`