Question

find the exact value of the expression. do not use a calculator.
\\( \cot \frac { 3 \pi } { 2 } - \cos \frac { 3 \pi } { 2 } \\)
select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. \\( \cot \frac { 3 \pi } { 2 } - \cos \frac { 3 \pi } { 2 } = \square \\)
(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 values of trigonometric functions

We know that \(\cot\theta=\frac{\cos\theta}{\sin\theta}\). For \(\theta = \frac{3\pi}{2}\), \(\sin\frac{3\pi}{2}=- 1\) and \(\cos\frac{3\pi}{2}=0\).

So, \(\cot\frac{3\pi}{2}=\frac{\cos\frac{3\pi}{2}}{\sin\frac{3\pi}{2}}=\frac{0}{-1} = 0\)

Step2: Calculate the expression

We need to find the value of \(\cot\frac{3\pi}{2}-\cos\frac{3\pi}{2}\)

Substitute \(\cot\frac{3\pi}{2} = 0\) and \(\cos\frac{3\pi}{2}=0\) into the expression:

\(\cot\frac{3\pi}{2}-\cos\frac{3\pi}{2}=0 - 0\)

Answer:

\(0\)