/*! 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 8 Evaluate the expression without ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 8

Evaluate the expression without using a calculator. $$ \arccos 0 $$

Short Answer

Expert verified
\(\arccos 0 = \pi/2\)

Step by step solution

01

Understanding the concept of the inverse trigonometric function

The function \(\arccos x\) is defined as the inverse function of \(\cos x\). Basically, it undoes the operation of the cosine function. If \(\cos x = y\), then \(\arccos y = x\). Knowing this, you need to find an angle \(x\) such that \(\cos x = 0\). Remember, the range of \(\arccos\) is \([0, \pi]\). So the angle you're looking for must be in this interval.
02

Finding the angle

Within the range of \([0, \pi]\), the angle at which the cosine value is zero is \(\pi/2\) or 90 degrees in degrees measurement because \(\cos(\pi/2) = 0\). Therefore, \(\arccos 0 = \pi/2\).

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

Sketch the graph of the function. Include two full periods. $$ y=2 \csc (x-\pi) $$

Use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$ y=\frac{4}{x}+\sin 2 x, \quad x>0 $$

Use a graphing utility to graph \(f, g\), and \(y=x\) in the same viewing window to verify geometrically that \(g\) is the inverse function of \(f\). (Be sure to restrict the domain of \(f\) properly.) $$ f(x)=\tan x, \quad g(x)=\arctan x $$

Sketch the graph of the function. Include two full periods. $$ y=\csc \frac{x}{3} $$

Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\). (a) As \(x \rightarrow 0^{+}\), the value of \(f(x) \rightarrow\) (b) As \(x \rightarrow 0^{-}\), the value of \(f(x) \rightarrow\) (c) As \(x \rightarrow \pi^{+}\), the value of \(f(x) \rightarrow\) (d) As \(x \rightarrow \pi^{-}\), the value of \(f(x) \rightarrow\) $$ f(x)=\cot x $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.