Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. tan(u) = 5/3, 0
Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. tan(u) = 5/3, 0
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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![**Problem Statement**
Use the given conditions to find the exact values of \( \sin(2u) \), \( \cos(2u) \), and \( \tan(2u) \) using the double-angle formulas.
\[
\tan(u) = \frac{5}{3}, \quad 0 < u < \frac{\pi}{2}
\]
**Double-Angle Values to Find:**
\[
\sin(2u) = \boxed{}
\]
\[
\cos(2u) = \boxed{}
\]
\[
\tan(2u) = \boxed{}
\]
**Instructions**
- Use trigonometric identities to solve the problem.
- Recall the double-angle formulas for sine, cosine, and tangent:
- \( \sin(2u) = 2 \sin(u) \cos(u) \)
- \( \cos(2u) = \cos^2(u) - \sin^2(u) \)
- \( \tan(2u) = \frac{2 \tan(u)}{1 - \tan^2(u)} \)
Apply these formulas to find the exact values based on the given condition for \( \tan(u) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa72a2e2b-0c6d-4164-ad48-805f970b7961%2Fada69203-c7bd-45f4-a825-100ede71f37f%2Flkfppoo_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Use the given conditions to find the exact values of \( \sin(2u) \), \( \cos(2u) \), and \( \tan(2u) \) using the double-angle formulas.
\[
\tan(u) = \frac{5}{3}, \quad 0 < u < \frac{\pi}{2}
\]
**Double-Angle Values to Find:**
\[
\sin(2u) = \boxed{}
\]
\[
\cos(2u) = \boxed{}
\]
\[
\tan(2u) = \boxed{}
\]
**Instructions**
- Use trigonometric identities to solve the problem.
- Recall the double-angle formulas for sine, cosine, and tangent:
- \( \sin(2u) = 2 \sin(u) \cos(u) \)
- \( \cos(2u) = \cos^2(u) - \sin^2(u) \)
- \( \tan(2u) = \frac{2 \tan(u)}{1 - \tan^2(u)} \)
Apply these formulas to find the exact values based on the given condition for \( \tan(u) \).
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