/*! 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 51 Write the trigonometric expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 51

Write the trigonometric expression as an algebraic expression. $$\sin (\arcsin x+\arccos x)$$

Short Answer

Expert verified
The algebraic expression for the given trigonometric expression is 1.

Step by step solution

01

Identify the Property

First, remember the special property that \(\arcsin x + \arccos x\) always equals \(\pi/2\). This property is derived from the fundamental relationship within a right-angle triangle where \(\sin^2 x + \cos^2 x = 1\).
02

Apply the Property

Now replace \(\arcsin x + \arccos x\) in the expression with \(\pi/2\). Therefore, the given trigonometric expression simplifies to \(\sin(\pi/2)\).
03

Compute the Expression

\(\sin(\pi/2)\) is 1, so the result of this expression is 1.

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

Verify the identity algebraically. Use a graphing utility to check your result graphically. $$\cos ^{2} 2 \alpha-\sin ^{2} 2 \alpha=\cos 4 \alpha$$

Find (if possible) the complement and supplement of each angle. (a) \(\frac{2 \pi}{7}\) (b) \(\frac{11 \pi}{15}\)

Find the solutions of the equation in the interval \([\mathbf{0}, \mathbf{2} \pi)\) Use a graphing utility to verify your answers. $$\cos 2 x-\cos 6 x=0$$

Use the sum-to-product formulas to write the sum or difference as a product. $$\sin 5 \theta-\sin \theta$$

Write the trigonometric expression as an algebraic expression. $$\cos (2 \arccos x)$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.