Question

find the exact value of the expression. do not use a calculator
cot(3π/2)+cos(3π/2)
select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. cot(3π/2)+cos(3π/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 the cotangent and cosine values

Recall the unit - circle definitions of trigonometric functions. The cotangent function is defined as $\cot\theta=\frac{\cos\theta}{\sin\theta}$, and we know that $\sin\frac{3\pi}{2}=- 1$, $\cos\frac{3\pi}{2}=0$.
So, $\cot\frac{3\pi}{2}=\frac{\cos\frac{3\pi}{2}}{\sin\frac{3\pi}{2}}=\frac{0}{-1}=0$.

Step2: Calculate the sum

We want to find the value of $\cot\frac{3\pi}{2}+\cos\frac{3\pi}{2}$.
Since $\cot\frac{3\pi}{2} = 0$ and $\cos\frac{3\pi}{2}=0$, then $\cot\frac{3\pi}{2}+\cos\frac{3\pi}{2}=0 + 0=0$.

Answer:

A. $\cot\frac{3\pi}{2}+\cos\frac{3\pi}{2}=0$