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QUESTION 1 One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. x in [22] sin x = 1/3₁ O COS X = - =--13, tan x = - ---5/22 O cos x = 1/2, tan x = -1/2 ○ cos x = =, tan x = <= ¹/²/² 12 -3, tan x = -¹/2 13 O cos x = --

QUESTION 1 One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. x in [22] sin x = 1/3₁ O COS X = - =--13, tan x = - ---5/22 O cos x = 1/2, tan x = -1/2 ○ cos x = =, tan x = <= ¹/²/² 12 -3, tan x = -¹/2 13 O cos x = --

Calculus: Early Transcendentals
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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### Trigonometric Functions and Their Relationships **QUESTION 1** One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. Given: \[ \sin x = \frac{12}{13}, \quad x \text{ in } \left[ \frac{\pi}{2}, \pi \right] \] Options: 1. \(\cos x = -\frac{5}{13}, \tan x = -\frac{5}{12}\) 2. \(\cos x = \frac{5}{13}, \tan x = -\frac{5}{12}\) 3. \(\cos x = \frac{5}{13}, \tan x = \frac{12}{5}\) 4. \(\cos x = -\frac{5}{13}, \tan x = -\frac{12}{5}\) ### Explanation of Options: - **Option 1**: - \(\cos x = -\frac{5}{13}\) - \(\tan x = -\frac{5}{12}\) - **Option 2**: - \(\cos x = \frac{5}{13}\) - \(\tan x = -\frac{5}{12}\) - **Option 3**: - \(\cos x = \frac{5}{13}\) - \(\tan x = \frac{12}{5}\) - **Option 4**: - \(\cos x = -\frac{5}{13}\) - \(\tan x = -\frac{12}{5}\) ### Analysis: Since \(\sin x = \frac{12}{13}\), and considering the interval \(\left[ \frac{\pi}{2}, \pi \right]\): - In this interval, \(\sin x\) is positive, \(\cos x\) is negative, and \(\tan x = \frac{\sin x}{\cos x}\) will be negative. Therefore, the correct answer is: - **Option 1**: (Because it fits the positive sine and negative cosine and tangent values for this interval)
Transcribed Image Text:### Trigonometric Functions and Their Relationships **QUESTION 1** One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. Given: \[ \sin x = \frac{12}{13}, \quad x \text{ in } \left[ \frac{\pi}{2}, \pi \right] \] Options: 1. \(\cos x = -\frac{5}{13}, \tan x = -\frac{5}{12}\) 2. \(\cos x = \frac{5}{13}, \tan x = -\frac{5}{12}\) 3. \(\cos x = \frac{5}{13}, \tan x = \frac{12}{5}\) 4. \(\cos x = -\frac{5}{13}, \tan x = -\frac{12}{5}\) ### Explanation of Options: - **Option 1**: - \(\cos x = -\frac{5}{13}\) - \(\tan x = -\frac{5}{12}\) - **Option 2**: - \(\cos x = \frac{5}{13}\) - \(\tan x = -\frac{5}{12}\) - **Option 3**: - \(\cos x = \frac{5}{13}\) - \(\tan x = \frac{12}{5}\) - **Option 4**: - \(\cos x = -\frac{5}{13}\) - \(\tan x = -\frac{12}{5}\) ### Analysis: Since \(\sin x = \frac{12}{13}\), and considering the interval \(\left[ \frac{\pi}{2}, \pi \right]\): - In this interval, \(\sin x\) is positive, \(\cos x\) is negative, and \(\tan x = \frac{\sin x}{\cos x}\) will be negative. Therefore, the correct answer is: - **Option 1**: (Because it fits the positive sine and negative cosine and tangent values for this interval)
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