Question

find the exact value of cot (-\frac{\pi}{2}). do not use a calculator.
cot (-\frac{\pi}{2}) = □
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall cotangent identity

$\cot(x)=\frac{\cos(x)}{\sin(x)}$.

Step2: Evaluate for $x =-\frac{\pi}{2}$

$\cos(-\frac{\pi}{2}) = 0$ and $\sin(-\frac{\pi}{2})=- 1$.
So, $\cot(-\frac{\pi}{2})=\frac{\cos(-\frac{\pi}{2})}{\sin(-\frac{\pi}{2})}=\frac{0}{-1}$.

Answer:

$0$