/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 54 Use the sum-to-product formulas ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 54

Use the sum-to-product formulas to rewrite the sum or difference as a product. $$\sin 3 \theta+\sin \theta$$

Short Answer

Expert verified
The sum \( \sin 3 \theta + \sin \theta \) can be rewritten as a product using the sum-to-product formula for sine, resulting in \( 2 \sin(2 \theta) \cos(\theta) \).

Step by step solution

01

Identification of A and B

Here we have two sine terms \( \sin 3 \theta \) and \( \sin \theta \). We need to match the form \( \sin(A + B) + \sin(A - B) \). So, we will take \( A = 2 \theta \) and \( B = \theta \). This would bring the given expression to the form of the sum-to-product formula.
02

Application of the sum-to-product formula

Now, let's apply the sum-to-product formula for sine. Hence \( \sin(A - B) + \sin(A + B) = 2 \sin A \cos B \). We substitute \( A = 2 \theta \) and \( B = \theta \) in the formula. So it becomes \( 2 \sin(2 \theta) \cos(\theta) \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find all solutions of the equation in the interval \([0,2 \pi)\). $$\sin (x+\pi)-\sin x+1=0$$

Find the exact value of the expression. $$\sin \frac{\pi}{12} \cos \frac{\pi}{4}+\cos \frac{\pi}{12} \sin \frac{\pi}{4}$$

(a) determine the quadrant in which \(u / 2\) lies, and (b) find the exact values of \(\sin (u / 2), \cos (u / 2),\) and \(\tan (u / 2)\) using the half-angle formulas. $$\cos u=7 / 25, \quad 0

Use the sum-to-product formulas to rewrite the sum or difference as a product. $$\cos 6 x+\cos 2 x$$

Find all solutions of the equation in the interval \([0,2 \pi) .\) Use a graphing utility to graph the equation and verify the solutions. $$\sin \frac{x}{2}+\cos x=0$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.