/*! 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 34 Use a double-angle formula to re... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 34

Use a double-angle formula to rewrite the expression. $$10 \sin ^{2} x-5$$

Short Answer

Expert verified
The expression \(10sin^2(x) - 5\), when rewritten using a double-angle formula, becomes \(-2cos(2x)\).

Step by step solution

01

Identify the formula to use

For this problem, the most useful double-angle formula will be \( cos(2x) = 1 - 2sin^2(x)\), because the given expression contains \(sin^2(x)\).
02

Rewrite the expression

We need to rewrite the expression \(10sin^2(x) - 5\) so that it matches the form of the double angle formula. To do this, the expression can be rewritten as \(2(5sin^2(x) - 5)\), which simplifies to \(2[(1 - cos(2x)) - 1]\). Distributing the 2 through the expression gives \(2 - 2cos(2x) - 2\). Since \(2 - 2 = 0\), the final equation is \(-2cos(2x)\). So, \(10sin^2(x) - 5\) can be rewritten as \(-2cos(2x)\).
03

Double check your work

It's always good practice to verify your answer. Make sure your final expression, \(-2cos(2x)\), matches up mathematically with your original expression, \(10sin^2(x) - 5\).

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 the \(x\) -intercepts of the graph. $$y=\tan ^{2}\left(\frac{\pi x}{6}\right)-3$$

Solve the multiple-angle equation. $$\sin \frac{x}{2}=-\frac{\sqrt{3}}{2}$$

Explain what would happen if you divided each side of the equation \(\cot x \cos ^{2} x=2 \cot x\) by \(\cot x .\) Is this a correct method to use when solving equations?

Use the Quadratic Formula to solve the equation in the interval \([0,2 \pi)\). Then use a graphing utility to approximate the angle \(x\). $$4 \cos ^{2} x-4 \cos x-1=0$$

The area of a rectangle (see figure) inscribed in one arc of the graph of \(y=\cos x\) is given by \(A=2 x \cos x, 0
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.