Math / Trigonometry

QuestionFill in the blank. The domain of $y=\cot x$ is all real numbers such that $\qquad$ $x \geq \pi$ $x \geq 0$ $x=n \pi$ , where $n$ is an integer $x \neq n \pi$ , where $n$ is an integer $x \neq \frac{n \pi}{2}$ , where $n$ is an odd integer

Studdy Solution

STEP 1

1. The function $y = \cot x$ is defined as $\cot x = \frac{\cos x}{\sin x}$ .
2. The function is undefined when the denominator is zero.
3. We need to find the values of $x$ where $\sin x = 0$ .

STEP 2

1. Determine where $\sin x = 0$ .
2. Identify the values of $x$ that make $\cot x$ undefined.
3. Determine the domain of $y = \cot x$ .

STEP 3

Determine where $\sin x = 0$ :
The sine function is zero at integer multiples of $\pi$ :
$\sin x = 0 \quad \text{when} \quad x = n\pi$
where $n$ is an integer.

STEP 4

Identify the values of $x$ that make $\cot x$ undefined:
Since $\cot x = \frac{\cos x}{\sin x}$ , it is undefined when $\sin x = 0$ .
Thus, $\cot x$ is undefined at:
$x = n\pi$
where $n$ is an integer.

STEP 5

Determine the domain of $y = \cot x$ :
The domain of $y = \cot x$ is all real numbers except where it is undefined. Therefore, the domain is:
$x \neq n\pi$
where $n$ is an integer.
The correct choice to fill in the blank is: $x \neq n \pi$ , where $n$ is an integer.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms