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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![The problem presented is to determine the values of the double-angle trigonometric functions for a given angle \( x \). Specifically, it states:
If \( \cos x = \frac{4}{5} \) and \( \csc x < 0 \), then determine the following:
1. \( \sin 2x = \) [input field];
2. \( \cos 2x = \) [input field];
3. \( \tan 2x = \) [input field].
The condition \( \csc x < 0 \) suggests that \( x \) is in a quadrant where the sine function is negative. Using these conditions, you are to calculate:
- \( \sin 2x = 2 \sin x \cos x \)
- \( \cos 2x = 2\cos^2 x - 1 \)
- \( \tan 2x = \frac{\sin 2x}{\cos 2x} \)
Make sure that all calculations are consistent with the angle being in the correct quadrant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F868a7cc3-2ad7-4fe7-9a39-259d78c013d4%2F92cab813-1801-4c04-b45c-bdd3223a8cab%2Fyy3m8ls_processed.png&w=3840&q=75)
Transcribed Image Text:The problem presented is to determine the values of the double-angle trigonometric functions for a given angle \( x \). Specifically, it states:
If \( \cos x = \frac{4}{5} \) and \( \csc x < 0 \), then determine the following:
1. \( \sin 2x = \) [input field];
2. \( \cos 2x = \) [input field];
3. \( \tan 2x = \) [input field].
The condition \( \csc x < 0 \) suggests that \( x \) is in a quadrant where the sine function is negative. Using these conditions, you are to calculate:
- \( \sin 2x = 2 \sin x \cos x \)
- \( \cos 2x = 2\cos^2 x - 1 \)
- \( \tan 2x = \frac{\sin 2x}{\cos 2x} \)
Make sure that all calculations are consistent with the angle being in the correct quadrant.
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