**1. Determine whether each of the statements below is true or false. Circle the appropriate answer and justify your answer by providing an explanation.**a. The angles $ \frac{25\pi}{4} $ and $ \frac{\pi}{4} $ are coterminal. - **True/False** - **Explanation:**b. $ \tan^{-1} x = \frac{1}{\tan x} $ - **True/False** - **Explanation:**c. $ \cos^{-1} \left( \cos \left( \frac{5\pi}{3} \right) \right) = \frac{5\pi}{3} $ - **True/False** - **Explanation:**d. The equation $ \sin x = -3 $ is an identity. - **True/False** - **Explanation:**

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Description: **1. Determine whether each of the statements below is true or false. Circle the appropriate answer and justify your answer by providing an explanation.**a. The angles $ \frac{25\pi}{4} $ and $ \frac{\pi}{4} $ are coterminal. - **True/False**

Determine whether the statements are true or false. a. 25π4,π4 b. tan-1x=1tanx c. cos-1cos5π3=5π3 d.…

Answered: and are coterminal. True/Fals 4

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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**1. Determine whether each of the statements below is true or false. Circle the appropriate answer and justify your answer by providing an explanation.**

a. The angles $ \frac{25\pi}{4} $ and $ \frac{\pi}{4} $ are coterminal.
- **True/False**
- **Explanation:**

b. $ \tan^{-1} x = \frac{1}{\tan x} $
- **True/False**
- **Explanation:**

c. $ \cos^{-1} \left( \cos \left( \frac{5\pi}{3} \right) \right) = \frac{5\pi}{3} $
- **True/False**
- **Explanation:**

d. The equation $ \sin x = -3 $ is an identity.
- **True/False**
- **Explanation:**

Expert Solution

Step 1

Determine whether the statements are true or false.

a. $\frac{25 π}{4}, \frac{π}{4}$

b. $\tan^{- 1} (x) = \frac{1}{\tan x}$

c. $\cos^{- 1} (\cos (\frac{5 π}{3})) = \frac{5 π}{3}$

d. The equation $\sin x = - 3$ is an identity.

Co-terminal angle:

Two angles are co-terminal if they are drawn in the standard position and both have their terminal sides in the same location.

The formulas are:

$\cos^{- 1} (\cos (x)) = x \tan x = \frac{1}{c o t x} \tan^{- 1} x = c o t^{- 1} (\frac{1}{x})$

Step 2

$a . \frac{25 π}{4} = \frac{180}{π} . \frac{25 π}{4} = 1125 ° \frac{π}{4} = 45 ° 1125 ° = 90 ° \times 12 + 45 ° = which belongs to 1st quadrant. So 1125° and 45° both terminal sides are on the first quadrant. So the statement is true. Both angles are co-terminal angle.$

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