Prove the following identity. 3 sin 0 - 4 sin' e sin 30 We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines. sin 30= sin (cos 0)(cos 20)(sin 0) sin (cos 0) + (1 - 2 sin 0) (sin 0) 2 sin 0 = 2 sin3 0 sin e = 2 sin 0 sin 0 2 sin e = (2 sin 0)1 - sin 0 2 sin e = 2 sin 0 - = 3 sin 0 - 4 sin5 e
Prove the following identity. 3 sin 0 - 4 sin' e sin 30 We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines. sin 30= sin (cos 0)(cos 20)(sin 0) sin (cos 0) + (1 - 2 sin 0) (sin 0) 2 sin 0 = 2 sin3 0 sin e = 2 sin 0 sin 0 2 sin e = (2 sin 0)1 - sin 0 2 sin e = 2 sin 0 - = 3 sin 0 - 4 sin5 e
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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Transcribed Image Text:Prove the following identity.
3 sin 0 - 4 sin' e
sin 30
We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a
Pythagorean Identity to write the expression in terms of sines.
sin 30= sin
(cos 0)(cos 20)(sin 0)
sin
(cos 0) + (1 - 2 sin 0) (sin 0)
2 sin 0
=
2 sin3 0
sin e
= 2 sin 0
sin 0 2 sin e
= (2 sin 0)1 -
sin 0 2 sin e
= 2 sin 0 -
= 3 sin 0 - 4 sin5 e
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