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use the given Corditions 10 find the exact values. of sin(2u) cosQu)rtancz) usingthe doube Aingk ngle formilas sıncau)= %3D Cos(2u)= tan(zu)=

use the given Corditions 10 find the exact values. of sin(2u) cosQu)rtancz) usingthe doube Aingk ngle formilas sıncau)= %3D Cos(2u)= tan(zu)=

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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**Title: Using Double Angle Formulas to Find Exact Values** **Instructions:** Use the given conditions to find the exact values of \(\sin(2u)\), \(\cos(2u)\), and \(\tan(2u)\) using the double angle formulas. **Conditions:** - \(\tan(u) = \frac{3}{5}\) - \(0 < u < \frac{\pi}{2}\) **Solution:** 1. **\(\sin(2u) =\)** 2. **\(\cos(2u) =\)** 3. **\(\tan(2u) =\)** By applying the double angle formulas for sine, cosine, and tangent: - \(\sin(2u) = 2\sin(u)\cos(u)\) - \(\cos(2u) = \cos^2(u) - \sin^2(u)\) - \(\tan(2u) = \frac{2\tan(u)}{1-\tan^2(u)}\) **Note:** Given that \(\tan(u) = \frac{\sin(u)}{\cos(u)} = \frac{3}{5}\), you can derive \(\sin(u)\) and \(\cos(u)\) through trigonometric identities or a right triangle setup.
Transcribed Image Text:**Title: Using Double Angle Formulas to Find Exact Values** **Instructions:** Use the given conditions to find the exact values of \(\sin(2u)\), \(\cos(2u)\), and \(\tan(2u)\) using the double angle formulas. **Conditions:** - \(\tan(u) = \frac{3}{5}\) - \(0 < u < \frac{\pi}{2}\) **Solution:** 1. **\(\sin(2u) =\)** 2. **\(\cos(2u) =\)** 3. **\(\tan(2u) =\)** By applying the double angle formulas for sine, cosine, and tangent: - \(\sin(2u) = 2\sin(u)\cos(u)\) - \(\cos(2u) = \cos^2(u) - \sin^2(u)\) - \(\tan(2u) = \frac{2\tan(u)}{1-\tan^2(u)}\) **Note:** Given that \(\tan(u) = \frac{\sin(u)}{\cos(u)} = \frac{3}{5}\), you can derive \(\sin(u)\) and \(\cos(u)\) through trigonometric identities or a right triangle setup.
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