Question

When working in decimal radians, how do you find the cot^-1(-5)?

Answer 1

Use your calculator and compute it as `cot^{-1}(-5)=tan^{-1}(-1/5) approx -0.197396` radians.

Explanation:

Since `cot(theta)=1/tan(theta)`, it follows that `cot^{-1}(5)` can be thought of as an angle `theta` in a right triangle where the ratio of the adjacent side over the opposite side is `5=5/1`. Therefore, the tangent of that angle `theta` is `1/5` (opposite over adjacent).

Now the tangent function is an odd function, so `tan(-theta)=-1/5` and therefore `tan^{-1}(-1/5)=-theta`. It follows that `tan^{-1}(-1/5)` is the answer you want. Now use your calculator (in radian mode).