/*! 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 26 Write each expression as the sin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 26

Write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression. $$\sin 40^{\circ} \cos 20^{\circ}+\cos 40^{\circ} \sin 20^{\circ}$$

Short Answer

Expert verified
The expression \(\sin 40^{\circ} \cos 20^{\circ}+\cos 40^{\circ} \sin 20^{\circ}\) simplifies to \(\sin60^{\circ}\), which is equal to \(\frac{\sqrt{3}}{2}\).

Step by step solution

01

Identify the appropriate identity

Recognize the given expression \(\sin 40^{\circ} \cos 20^{\circ}+\cos 40^{\circ} \sin 20^{\circ}\) as a form of the trigonometric identity \(\sin(a) \cos(b) + \cos(a) \sin(b) = \sin(a+b)\). Here, a is \(40^{\circ}\) and b is \(20^{\circ}\).
02

Apply the identity

Substitute the values of a and b into the identity. This simplifies the expression as \(\sin(40^{\circ}+20^{\circ}) = \sin60^{\circ}\).
03

Compute the value

The value of \(\sin60^{\circ}\) is \(\frac{\sqrt{3}}{2}\). Hence, the expression simplifies to \(\frac{\sqrt{3}}{2}\).

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

Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$\tan x=-6.2154$$

A hot-air balloon is rising vertically. From a point on level ground 120 feet from the point directly under the passenger compartment, the angle of elevation to the balloon changes from \(37.1^{\circ}\) to \(62.4^{\circ} .\) How far, to the nearest tenth of a foot, does the balloon rise during this period? (Section 4.8, Example 4 )

Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$7 \cos x=4-2 \sin ^{2} x$$

Find the exact value of each expression. Do not use a calculator. $$\sin \left[\sin ^{-1} \frac{3}{5}-\cos ^{-1}\left(-\frac{4}{5}\right)\right]$$

Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$2 \sin ^{2} x=3-\sin x$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.