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6.3 6.3 DOUBLE ANGLE FORMULAS 279 DOUBLE ANGLE FORMULAS 8 1. Use a Double Angle Formula to rewrite each expression. (a) cos 2(2x) (b) sin 3x (c) tan 6r (d) sinx (e) cos (f) tan(-7x) 2. Express as a single sine or cosine function. (a) 2 sin 30 cos 30 1 0 0 (c) sin 3. If cos 0 = COS 4. If sin = (e) 1 - 2 sin² (g) 8 sin² 20 - 4 4 5' 2 Determine the quadrant of angle 20. 12 13' the quadrant of angle 20. 2 - (b) 6 sin 0 cos 0 30 (d) cos 2 (f) 2 cos² 30 2 (1⁄º) — ₁ -1 (h) 1 - 2 sin³- 5. If sin 6 = 3,06 0 0€ - ≤0, find the value of sin 20 and cos 20. sin² 0505 7, e evaluate sin 20 and cos 20. Determine find the value of sin 40.

6.3 6.3 DOUBLE ANGLE FORMULAS 279 DOUBLE ANGLE FORMULAS 8 1. Use a Double Angle Formula to rewrite each expression. (a) cos 2(2x) (b) sin 3x (c) tan 6r (d) sinx (e) cos (f) tan(-7x) 2. Express as a single sine or cosine function. (a) 2 sin 30 cos 30 1 0 0 (c) sin 3. If cos 0 = COS 4. If sin = (e) 1 - 2 sin² (g) 8 sin² 20 - 4 4 5' 2 Determine the quadrant of angle 20. 12 13' the quadrant of angle 20. 2 - (b) 6 sin 0 cos 0 30 (d) cos 2 (f) 2 cos² 30 2 (1⁄º) — ₁ -1 (h) 1 - 2 sin³- 5. If sin 6 = 3,06 0 0€ - ≤0, find the value of sin 20 and cos 20. sin² 0505 7, e evaluate sin 20 and cos 20. Determine find the value of sin 40.

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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Please help me with questions 1 through 5 and show your work
**Double Angle Formulas** **6.3 DOUBLE ANGLE FORMULAS** --- **1. Use a Double Angle Formula to rewrite each expression.** (a) \( \cos 2(2x) \) (b) \( \sin 3x \) (c) \( \tan 6x \) (d) \( \sin \frac{1}{2}x \) (e) \( \cos \frac{3}{2}x \) (f) \( \tan(-7x) \) --- **2. Express as a single sine or cosine function.** (a) \( 2 \sin 30 \cos 30 \) (b) \( 6 \sin \theta \cos \theta \) (c) \( \frac{1}{2} \sin \frac{\theta}{2} \cos \frac{\theta}{2} \) (d) \( \cos^2 \frac{3\theta}{2} - \sin^2 \frac{3\theta}{2} \) (e) \( 1 - 2 \sin^2 \frac{\theta}{4} \) (f) \( 2 \cos^2 \left(\frac{7\theta}{2}\right) - 1 \) (g) \( 8 \sin^2 20^\circ - 4 \) (h) \( 1 - 2 \sin^2 \left(\frac{\pi}{4} - \frac{x}{2}\right) \) --- **3.** If \( \cos \theta = -\frac{4}{5}, \, \frac{\pi}{2} \leq \theta \leq \pi \), find the value of \( \sin 2\theta \) and \( \cos 2\theta \). Determine the quadrant of angle \( 2\theta \). --- **4.** If \( \sin \theta = \frac{12}{13}, \, 0 \leq \theta \leq \frac{\pi}{2} \), evaluate \( \sin 2\theta \) and \( \cos 2\theta \). Determine the quadrant of angle \( 2\theta \). --- **5.** If \( \sin \theta = \frac{2}{3}, \, 0 \leq \theta \leq \frac{\pi}{2} \), find the
Transcribed Image Text:**Double Angle Formulas** **6.3 DOUBLE ANGLE FORMULAS** --- **1. Use a Double Angle Formula to rewrite each expression.** (a) \( \cos 2(2x) \) (b) \( \sin 3x \) (c) \( \tan 6x \) (d) \( \sin \frac{1}{2}x \) (e) \( \cos \frac{3}{2}x \) (f) \( \tan(-7x) \) --- **2. Express as a single sine or cosine function.** (a) \( 2 \sin 30 \cos 30 \) (b) \( 6 \sin \theta \cos \theta \) (c) \( \frac{1}{2} \sin \frac{\theta}{2} \cos \frac{\theta}{2} \) (d) \( \cos^2 \frac{3\theta}{2} - \sin^2 \frac{3\theta}{2} \) (e) \( 1 - 2 \sin^2 \frac{\theta}{4} \) (f) \( 2 \cos^2 \left(\frac{7\theta}{2}\right) - 1 \) (g) \( 8 \sin^2 20^\circ - 4 \) (h) \( 1 - 2 \sin^2 \left(\frac{\pi}{4} - \frac{x}{2}\right) \) --- **3.** If \( \cos \theta = -\frac{4}{5}, \, \frac{\pi}{2} \leq \theta \leq \pi \), find the value of \( \sin 2\theta \) and \( \cos 2\theta \). Determine the quadrant of angle \( 2\theta \). --- **4.** If \( \sin \theta = \frac{12}{13}, \, 0 \leq \theta \leq \frac{\pi}{2} \), evaluate \( \sin 2\theta \) and \( \cos 2\theta \). Determine the quadrant of angle \( 2\theta \). --- **5.** If \( \sin \theta = \frac{2}{3}, \, 0 \leq \theta \leq \frac{\pi}{2} \), find the
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