Question

find the exact value of the expression. do not use a calculator. cot(π/2)+sin(π/2) select the correct choice and, if necessary, fill in the answer box to complete your choice. a. cot(π/2)+sin(π/2)=□ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the answer is undefined.

Explanation:

Step1: Recall cotangent and sine values

Recall the unit - circle values. $\cot\theta=\frac{\cos\theta}{\sin\theta}$. For $\theta = \frac{\pi}{2}$, $\cos\frac{\pi}{2}=0$ and $\sin\frac{\pi}{2}=1$. So, $\cot\frac{\pi}{2}=\frac{\cos\frac{\pi}{2}}{\sin\frac{\pi}{2}}=\frac{0}{1} = 0$. Also, $\sin\frac{\pi}{2}=1$.

Step2: Calculate the sum

Add the values of $\cot\frac{\pi}{2}$ and $\sin\frac{\pi}{2}$. We have $\cot\frac{\pi}{2}+\sin\frac{\pi}{2}=0 + 1=1$.

Answer:

A. $\cot\frac{\pi}{2}+\sin\frac{\pi}{2}=1$