Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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**Question:** Which of the following is not in the domain of \( \cot(x) \)? Select all correct answers. **Options:** - [ ] \( -\pi \) - [ ] \( \frac{\pi}{6} \) - [ ] \( \frac{\pi}{2} \) - [ ] \( \frac{3\pi}{2} \) - [ ] \( 0 \) **Explanation:** The cotangent function, \( \cot(x) \), is undefined where the sine of \( x \) is zero. These points occur at integer multiples of \( \pi \) (e.g., \( 0, \pi, -\pi \), etc.). Therefore, values in the options that are multiples of \( \pi \) are not in the domain of \( \cot(x) \) because they would result in division by zero.
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Transcribed Image Text:**Question:** Which of the following is not in the domain of \( \cot(x) \)? Select all correct answers. **Options:** - [ ] \( -\pi \) - [ ] \( \frac{\pi}{6} \) - [ ] \( \frac{\pi}{2} \) - [ ] \( \frac{3\pi}{2} \) - [ ] \( 0 \) **Explanation:** The cotangent function, \( \cot(x) \), is undefined where the sine of \( x \) is zero. These points occur at integer multiples of \( \pi \) (e.g., \( 0, \pi, -\pi \), etc.). Therefore, values in the options that are multiples of \( \pi \) are not in the domain of \( \cot(x) \) because they would result in division by zero.
**Title: Finding Asymptotes of Trigonometric Functions** **Problem Statement:** Give the equation of an asymptote for the graph of \( f(x) = \tan 2x \) on the interval \( (0, \pi) \). **Instructions:** Enter your answer as an equation, \( x = a \). If there is more than one answer, separate each equation with a comma, \( x = a, x = b \). **Answer Input:** Provide your answer below: [Answer box]
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Transcribed Image Text:**Title: Finding Asymptotes of Trigonometric Functions** **Problem Statement:** Give the equation of an asymptote for the graph of \( f(x) = \tan 2x \) on the interval \( (0, \pi) \). **Instructions:** Enter your answer as an equation, \( x = a \). If there is more than one answer, separate each equation with a comma, \( x = a, x = b \). **Answer Input:** Provide your answer below: [Answer box]
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