Stitz-Zeager_College_Algebra_e-book

Since we are given x cost we know sect 1 1 x the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: sin(β ) 10.4 Trigonometric Identities 659 Example 10.4.2. 1. Find the exact value of sin 19π 12 2. If α is a Quadrant II angle with sin(α) = find sin(α − β ). 5 13 , and β is a Quadrant III angle with tan(β ) = 2, 3. Derive a formula for tan(α + β ) in terms of tan(α) and tan(β ). Solution. 1. As in Example 10.4.1, we need to write the angle 19π as a sum or difference of common angles. 12 The denominator of 12 suggests a combination of angles with denominators 3 and 4. One π such combination is 19π = 43 + π . Applying Theorem 10.15, we get 12 4 sin 19π 12 4π π + 3 4 4π π 4π π = sin cos + cos sin 3 4 3 4 √ √ √ 3 2 1 2 = − +− 2 2 2 2 √ √ − 6− 2 = 4 = sin 2. In order to find sin(α − β ) using Theorem 10.15, we need to find cos(α) and both cos(β ) and sin(β ). To find cos(α), we use the Pythagorean Identity cos2 (α) + sin2 (α) = 1. Since 5 52 sin(α) = 13 , we have cos2 (α) + 13 = 1, or cos(α) = ± 12 . Since α is a Quadrant II angle, 13 cos(α)...
View Full Document

Ask a homework question - tutors are online