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angle in standard position when a functional value and a constraint are known. hine the values of the trigonometric functions of an In Exercises 1-5, find the values of the six trigonometric functions of with the given constraint. Function Value Constraint 1. tan (0) == 15 8 sin (0) > 0.

angle in standard position when a functional value and a constraint are known. hine the values of the trigonometric functions of an In Exercises 1-5, find the values of the six trigonometric functions of with the given constraint. Function Value Constraint 1. tan (0) == 15 8 sin (0) > 0.

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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**Objective #12:** Determine the values of the trigonometric functions of an angle in standard position when a functional value and a constraint are known. In Exercises 1-5, find the values of the six trigonometric functions of θ with the given constraint. | Function Value | Constraint | |-------------------------|--------------------------------| | 1. \( \tan(θ) = -\frac{15}{8} \) | \( \sin(θ) > 0 \) | | 2. \( \sin(θ) = \frac{3}{5} \) | θ lies in Quadrant II | | 3. \( \cot(θ) = -3 \) | \( \cos(θ) > 0 \) | | 4. \( \sec(θ) = -2 \) | \( \sin(θ) < 0 \) | | 5. \( \cot(θ) \) is undefined | \( \frac{\pi}{2} \leq θ \leq \frac{3\pi}{2} \) | ### Explanation - **Exercise 1:** Given \( \tan(θ) = -\frac{15}{8} \) and \( \sin(θ) > 0 \), find other trigonometric function values of θ. - **Exercise 2:** Given \( \sin(θ) = \frac{3}{5} \) and θ in Quadrant II, calculate all six trigonometric functions. - **Exercise 3:** Given \( \cot(θ) = -3 \) and \( \cos(θ) > 0 \), determine trigonometric functions of θ. - **Exercise 4:** With \( \sec(θ) = -2 \) and \( \sin(θ) < 0 \), find other trigonometric values. - **Exercise 5:** For \( \cot(θ) \) undefined and \( \frac{\pi}{2} \leq θ \leq \frac{3\pi}{2} \), calculate all trigonometric functions.
Transcribed Image Text:**Objective #12:** Determine the values of the trigonometric functions of an angle in standard position when a functional value and a constraint are known. In Exercises 1-5, find the values of the six trigonometric functions of θ with the given constraint. | Function Value | Constraint | |-------------------------|--------------------------------| | 1. \( \tan(θ) = -\frac{15}{8} \) | \( \sin(θ) > 0 \) | | 2. \( \sin(θ) = \frac{3}{5} \) | θ lies in Quadrant II | | 3. \( \cot(θ) = -3 \) | \( \cos(θ) > 0 \) | | 4. \( \sec(θ) = -2 \) | \( \sin(θ) < 0 \) | | 5. \( \cot(θ) \) is undefined | \( \frac{\pi}{2} \leq θ \leq \frac{3\pi}{2} \) | ### Explanation - **Exercise 1:** Given \( \tan(θ) = -\frac{15}{8} \) and \( \sin(θ) > 0 \), find other trigonometric function values of θ. - **Exercise 2:** Given \( \sin(θ) = \frac{3}{5} \) and θ in Quadrant II, calculate all six trigonometric functions. - **Exercise 3:** Given \( \cot(θ) = -3 \) and \( \cos(θ) > 0 \), determine trigonometric functions of θ. - **Exercise 4:** With \( \sec(θ) = -2 \) and \( \sin(θ) < 0 \), find other trigonometric values. - **Exercise 5:** For \( \cot(θ) \) undefined and \( \frac{\pi}{2} \leq θ \leq \frac{3\pi}{2} \), calculate all trigonometric functions.
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