9) Find csc 0 if sec 0 = 9-√5 2

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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# 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
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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