/*! 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 133 Write the trigonometric expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 133

Write the trigonometric expression as an algebraic expression. $$\cos (2 \arcsin x)$$

Short Answer

Expert verified
The algebraic expression for \(\cos (2 \arcsin x)\) is \(1 - 2x^{2}\).

Step by step solution

01

Replace with Double Angle Formula

Replace \(\cos(2\Theta)\) with \(1 - 2\sin^{2}\Theta\), where \(\Theta = \arcsin x\). So you get \(1 - 2\sin^{2}(\arcsin x)\).
02

Simplify the Expression

Since \(\sin(\arcsin x) = x\), the equation becomes \(1 - 2x^{2}\).
03

Check the Equation

Check that no trigonometric functions remain. The equation is simplified and only algebraic terms remain, so the process is complete.

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

Fill in the blank. \(\cos (u-v)=\)_____

Find the exact value of each expression. (a) \(\sin \left(\frac{3 \pi}{4}+\frac{5 \pi}{6}\right)\) (b) \(\sin \frac{3 \pi}{4}+\sin \frac{5 \pi}{6}\)

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

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

(a) use a graphing utility to graph the function and approximate the maximum and minimum points on the graph in the interval \([0,2 \pi),\) and (b) solve the trigonometric equation and demonstrate that its solutions are the \(x\) -coordinates of the maximum and minimum points of \(f .\) (Calculus is required to find the trigonometric equation.) Function $$f(x)=2 \sin x+\cos 2 x$$ Trigonometric Equation $$2 \cos x-4 \sin x \cos x=0$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Pure 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.