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In the right triangle shown to the right, the angle e is measured in radians. 1. Find tan 0. 2. Find tanx. 3. Find the hypotenuse of the triangle as a function of x. 4. Find sin (tan ') as a ratio involving no trig functions. 5. Find sec (tan '(x)) as a ratio involving no trig functions. 6. If x <0, then tan Verify that your answers to parts (4) and (S) are still valid in this case. x is a negative angle in the fourth quadrant (Figure 4.86).

In the right triangle shown to the right, the angle e is measured in radians. 1. Find tan 0. 2. Find tanx. 3. Find the hypotenuse of the triangle as a function of x. 4. Find sin (tan ') as a ratio involving no trig functions. 5. Find sec (tan '(x)) as a ratio involving no trig functions. 6. If x <0, then tan Verify that your answers to parts (4) and (S) are still valid in this case. x is a negative angle in the fourth quadrant (Figure 4.86).

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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**Exploration 1: Finding Inverse Trig Functions of Trig Functions** In the right triangle shown to the right, the angle \( \theta \) is measured in radians. 1. Find \( \tan \theta \). 2. Find \( \tan^{-1} x \). 3. Find the hypotenuse of the triangle as a function of \( x \). 4. Find \( \sin (\tan^{-1} x) \) as a ratio involving no trig functions. 5. Find \( \sec (\tan^{-1} x) \) as a ratio involving no trig functions. 6. If \( x < 0 \), then \( \tan^{-1} x \) is a negative angle in the fourth quadrant (Figure 4.86). Verify that your answers to parts (4) and (5) are still valid in this case. **Diagram Explanation:** The diagram is a right triangle with an angle \( \theta \), opposite side labeled as \( x \), and adjacent side labeled as 1.
Transcribed Image Text:**Exploration 1: Finding Inverse Trig Functions of Trig Functions** In the right triangle shown to the right, the angle \( \theta \) is measured in radians. 1. Find \( \tan \theta \). 2. Find \( \tan^{-1} x \). 3. Find the hypotenuse of the triangle as a function of \( x \). 4. Find \( \sin (\tan^{-1} x) \) as a ratio involving no trig functions. 5. Find \( \sec (\tan^{-1} x) \) as a ratio involving no trig functions. 6. If \( x < 0 \), then \( \tan^{-1} x \) is a negative angle in the fourth quadrant (Figure 4.86). Verify that your answers to parts (4) and (5) are still valid in this case. **Diagram Explanation:** The diagram is a right triangle with an angle \( \theta \), opposite side labeled as \( x \), and adjacent side labeled as 1.
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