Suppose in a right triangle, cos(t)=3/4. How do you find: cot(t)?
Starting from the fundamental equation
we can deduce
So, in our case,
Actually, we have
In fact, since
An acute angle lies in the first quadrant, where both sine and cosine are positive, hence the choice of the sign.
Now that we know both sine and cosine, we can compute the cotangent by its definition: