Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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My professor never uploaded the correct review answer key and the test is tomorrow! Any help appreciated.
![# Trigonometric Function Problems
### Find the value of the trig function indicated. (DRAW THE TRIANGLE)
1. Find \( \csc \theta \) if \( \sec \theta = \frac{\sqrt{5}}{2} \)
2. Find \( \cot \theta \) if \( \sec \theta = \frac{5}{3} \)
3. Find \( \csc \theta \) if \( \sec \theta = \frac{5}{4} \)
4. Find \( \cot \theta \) if \( \csc \theta = \frac{25}{7} \)
5. Find \( \csc \theta \) if \( \cot \theta = \frac{7}{23} \)
6. Find \( \csc \theta \) if \( \cot \theta = \frac{2\sqrt{5}}{15} \)
### Circular Motion Problems
Suppose that point \( P \) is on a circle with radius \( r \), and ray \( OP \) is rotating with angular speed \( \omega \). Use the given values of \( r, \omega \), and \( t \) to do the following. See Example 6.
- **(a)** Find the angle generated by \( P \) in time \( t \).
- **(b)** Find the distance traveled by \( P \) along the circle in time \( t \).
- **(c)** Find the linear speed of \( P \).
### Given Values
83. \[ r = 20 \, \text{cm}, \, \omega = \frac{17}{2} \, \text{radians per sec}, \, t = 6 \, \text{sec} \]
84. \[ r = 30 \, \text{cm}, \omega = \frac{\pi}{10} \, \text{radian per sec}, t = 4 \, \text{sec} \]
85. \[ r = 8 \, \text{in.}, \omega = \frac{5\pi}{3} \, \text{radians per min}, t = 9 \, \text{min} \]
86. \[ r = 12 \, \text{ft}, \omega = 8\pi \, \text{radians per](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f291453-8071-45aa-8e9f-8fe473f07ff7%2F8299fa90-11c0-4fde-87ce-1c1253c72183%2Fylvmx2b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Trigonometric Function Problems
### Find the value of the trig function indicated. (DRAW THE TRIANGLE)
1. Find \( \csc \theta \) if \( \sec \theta = \frac{\sqrt{5}}{2} \)
2. Find \( \cot \theta \) if \( \sec \theta = \frac{5}{3} \)
3. Find \( \csc \theta \) if \( \sec \theta = \frac{5}{4} \)
4. Find \( \cot \theta \) if \( \csc \theta = \frac{25}{7} \)
5. Find \( \csc \theta \) if \( \cot \theta = \frac{7}{23} \)
6. Find \( \csc \theta \) if \( \cot \theta = \frac{2\sqrt{5}}{15} \)
### Circular Motion Problems
Suppose that point \( P \) is on a circle with radius \( r \), and ray \( OP \) is rotating with angular speed \( \omega \). Use the given values of \( r, \omega \), and \( t \) to do the following. See Example 6.
- **(a)** Find the angle generated by \( P \) in time \( t \).
- **(b)** Find the distance traveled by \( P \) along the circle in time \( t \).
- **(c)** Find the linear speed of \( P \).
### Given Values
83. \[ r = 20 \, \text{cm}, \, \omega = \frac{17}{2} \, \text{radians per sec}, \, t = 6 \, \text{sec} \]
84. \[ r = 30 \, \text{cm}, \omega = \frac{\pi}{10} \, \text{radian per sec}, t = 4 \, \text{sec} \]
85. \[ r = 8 \, \text{in.}, \omega = \frac{5\pi}{3} \, \text{radians per min}, t = 9 \, \text{min} \]
86. \[ r = 12 \, \text{ft}, \omega = 8\pi \, \text{radians per
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