Question

Given `tantheta=2, sintheta<0` to find the remaining trigonometric function?

Answer 1

See explanation.

Explanation:

As `tan theta = 2 > 0`, sine and cosine have the same sign. So,

`(sin theta, cos theta) = +-1/sqrt5(2, 1).`

`(csc theta, sec theta)=(1/sin theta, 1/ cos theta)= +- sqrt5/2(1, 2)`

`cot theta = 1/tan theta=1/2`.