Questions: What is the y-intercept of y=cot x ?

Transcript text: What is the $y$-intercept of $y=\cot x$ ?

Solution

Solution Steps

To find the $y$-intercept of the function $ y = \cot x $, we need to determine the value of $ y $ when $ x = 0 $. The cotangent function is defined as $ \cot x = \frac{\cos x}{\sin x} $. We will evaluate this at $ x = 0 $.

Step 1: Evaluate $ \cot(0) $

To find the $ y $-intercept of the function $ y = \cot x $, we evaluate $ y $ at $ x = 0 $: \[ y = \cot(0) = \frac{\cos(0)}{\sin(0)} \]

Step 2: Determine the Values of $ \cos(0) $ and $ \sin(0) $

We know that: \[ \cos(0) = 1 \quad \text{and} \quad \sin(0) = 0 \]

Step 3: Analyze the Result

Substituting these values into the cotangent expression gives: \[ y = \frac{1}{0} \] This expression is undefined, indicating that $ \cot(0) $ does not have a finite value.

Final Answer

Since the $ y $-intercept of $ y = \cot x $ is undefined, we conclude that there is no $ y $-intercept. Thus, the answer is: \[ \boxed{\text{undefined}} \]

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