Question

Evaluate cot 45° without using a calculator by using ratios in a reference triangle.

Answer 1

Since we are looking for $\cot 45^\circ$, we must use a $45^\circ-45^\circ-90^\circ$ triangle. In a $45^\circ-45^\circ-90^\circ$ reference triangle, the legs are both $1$, and the hypotenuse is $\sqrt{2}$. The function is cotangent, so we are looking for the adjacent side divided by the opposite side of one of the $45^\circ$ angles. Both the adjacent and the opposite sides are the legs regardless of which $45^\circ$ angle you choose, so we get $\frac{1}{1} =1$, the answer.