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Find the exact value of the cosine and sine of the angle: : Use Section 2 in Chapter 10 of the book to answer the following: If cos(e) = 5/13 with e in Quadrant IV, what is the sin(e)? Find all angles that satisfy the equation: cos(e) = ½ Find the measurement of the missing angle, 0, and the lengths of the missing sides, b and c: b 30° 2.

Find the exact value of the cosine and sine of the angle: : Use Section 2 in Chapter 10 of the book to answer the following: If cos(e) = 5/13 with e in Quadrant IV, what is the sin(e)? Find all angles that satisfy the equation: cos(e) = ½ Find the measurement of the missing angle, 0, and the lengths of the missing sides, b and c: b 30° 2.

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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### Trigonometry Problems and Solutions #### Problem 1: Exact Values of Cosine and Sine **Question:** Find the exact value of the cosine and sine of the angle: \( \Theta = \frac{5\pi}{6} \). #### Problem 2: Sine given Cosine in Quadrant IV **Question:** Use Section 2 in Chapter 10 of the book to answer the following: If \( \cos(\Theta) = \frac{5}{13} \) with \( \Theta \) in Quadrant IV, what is the \( \sin(\Theta) \)? #### Problem 3: Angles Satisfying Cosine Equation **Question:** Find all angles that satisfy the equation: \( \cos(\Theta) = \frac{1}{2} \). #### Problem 4: Finding Missing Angle and Sides **Question:** Find the measurement of the missing angle, \( \theta \), and the lengths of the missing sides, \( b \) and \( c \): - The triangle is a right triangle. - One angle is \( 30^\circ \). - The adjacent side to the \( 30^\circ \) angle is 2 units long. **Diagram Explanation:** - The triangle has three sides: \( b \) (opposite to the angle \( \theta \)), \( c \) (hypotenuse), and 2 (adjacent to the \( 30^\circ \) angle). - The right angle is between sides \( b \) and 2. - One angle is labeled \( \theta \). - The hypotenuse \( c \) is the side opposite the right angle. ### Solutions 1. **Exact Values of Cosine and Sine for \( \Theta = \frac{5\pi}{6} \):** - \( \cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2} \) - \( \sin\left(\frac{5\pi}{6}\right) = \frac{1}{2} \) 2. **Sine given Cosine in Quadrant IV:** - Given \( \cos(\Theta) = \frac{5}{13} \) in Quadrant IV - \( \sin^2(\Theta) + \cos^2(\Theta) = 1
Transcribed Image Text:### Trigonometry Problems and Solutions #### Problem 1: Exact Values of Cosine and Sine **Question:** Find the exact value of the cosine and sine of the angle: \( \Theta = \frac{5\pi}{6} \). #### Problem 2: Sine given Cosine in Quadrant IV **Question:** Use Section 2 in Chapter 10 of the book to answer the following: If \( \cos(\Theta) = \frac{5}{13} \) with \( \Theta \) in Quadrant IV, what is the \( \sin(\Theta) \)? #### Problem 3: Angles Satisfying Cosine Equation **Question:** Find all angles that satisfy the equation: \( \cos(\Theta) = \frac{1}{2} \). #### Problem 4: Finding Missing Angle and Sides **Question:** Find the measurement of the missing angle, \( \theta \), and the lengths of the missing sides, \( b \) and \( c \): - The triangle is a right triangle. - One angle is \( 30^\circ \). - The adjacent side to the \( 30^\circ \) angle is 2 units long. **Diagram Explanation:** - The triangle has three sides: \( b \) (opposite to the angle \( \theta \)), \( c \) (hypotenuse), and 2 (adjacent to the \( 30^\circ \) angle). - The right angle is between sides \( b \) and 2. - One angle is labeled \( \theta \). - The hypotenuse \( c \) is the side opposite the right angle. ### Solutions 1. **Exact Values of Cosine and Sine for \( \Theta = \frac{5\pi}{6} \):** - \( \cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2} \) - \( \sin\left(\frac{5\pi}{6}\right) = \frac{1}{2} \) 2. **Sine given Cosine in Quadrant IV:** - Given \( \cos(\Theta) = \frac{5}{13} \) in Quadrant IV - \( \sin^2(\Theta) + \cos^2(\Theta) = 1
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