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Find the exact value of the indicated trigonometric function of 0. 4) sin 0 tan 0 >0 Find sec 0. A) V7 B) 4/33 C) 733 D). 33 4 33 33 7

Find the exact value of the indicated trigonometric function of 0. 4) sin 0 tan 0 >0 Find sec 0. A) V7 B) 4/33 C) 733 D). 33 4 33 33 7

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Trigonometry Problem: Finding the Exact Value of sec θ** Objective: Find the exact value of the indicated trigonometric function of θ. Given: - \( \sin \theta = -\frac{4}{7} \) - \( \tan \theta > 0 \) Task: Determine the value of \( \sec \theta \). Options: A) \( \frac{\sqrt{7}}{4} \) B) \(-\frac{4\sqrt{33}}{33}\) C) \(\frac{7\sqrt{33}}{33}\) D) \(-\frac{\sqrt{33}}{7}\) **Explanation:** - We are dealing with a trigonometric function where the sine value is negative, and the tangent value is positive. This implies that θ is in the third quadrant, where sine is negative, and tangent is positive. - The secant function, sec θ, is the reciprocal of the cosine function. **Solution Steps:** 1. Start by using the Pythagorean identity to find cos θ. 2. Use the given conditions to solve for the exact value of sec θ. 3. Choose the correct option from A, B, C, or D based on calculations.
Transcribed Image Text:**Trigonometry Problem: Finding the Exact Value of sec θ** Objective: Find the exact value of the indicated trigonometric function of θ. Given: - \( \sin \theta = -\frac{4}{7} \) - \( \tan \theta > 0 \) Task: Determine the value of \( \sec \theta \). Options: A) \( \frac{\sqrt{7}}{4} \) B) \(-\frac{4\sqrt{33}}{33}\) C) \(\frac{7\sqrt{33}}{33}\) D) \(-\frac{\sqrt{33}}{7}\) **Explanation:** - We are dealing with a trigonometric function where the sine value is negative, and the tangent value is positive. This implies that θ is in the third quadrant, where sine is negative, and tangent is positive. - The secant function, sec θ, is the reciprocal of the cosine function. **Solution Steps:** 1. Start by using the Pythagorean identity to find cos θ. 2. Use the given conditions to solve for the exact value of sec θ. 3. Choose the correct option from A, B, C, or D based on calculations.
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