/*! 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 105 Determine whether the statement ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 105

Determine whether the statement is true or false. Justify your answer. \(\arctan x=\frac{\arcsin x}{\arccos x}\)

Short Answer

Expert verified
The statement \(\arctan x=\frac{\arcsin x}{\arccos x}\) is indeed true.

Step by step solution

01

Recall definitions

Here, it's important to remember the foundational properties of arccos, arcsin, and arctan functions.
02

Convert to Cotangent

Next, to simplify the comparison, we convert \(\arctan x\) into \(\frac{1}{\tan x}\), and \(\frac{\arcsin x}{\arccos x}\) into \(\frac{1}{\cos x}\) and \(\frac{1}{\sin x}\) respectively.
03

Use Trigonometric Tautology

The relation \(\sin(x)^2 + \cos(x)^2 = 1\) is well known, so we can safely combine our expression into \(\frac{1}{\sin x}\) and \(\frac{cos x}{sin x}\) which results in cotangent.
04

Examine the Results

In the end, we will see that the left side \(\frac{1}{\tan x}\) is indeed equal to \(\frac{cos x}{sin x}\) which stands for the right side.

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

A company that produces wakeboards forecasts monthly sales \(S\) during a two- year period to be $$S=2.7+0.142 t+2.2 \sin \left(\frac{\pi t}{6}-\frac{\pi}{2}\right)$$ where \(S\) is measured in hundreds of units and \(t\) is the time (in months), with \(t=1\) corresponding to January \(2014 .\) Estimate sales for each month. (a) January 2014 (b) February 2015 (c) May 2014 (d) June 2015

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. Identify any asymptote of the graph. $$f(x)=e^{3 x}$$

Finding the Domain of a Function Find the domain of the function. $$h(x)=\frac{x}{x^{2}-9}$$

Prove the identity \(\arctan (-x)=-\arctan x\)

Define the inverse cosecant function by restricting the domain of the cosecant function to the intervals \([-\pi / 2,0)\) and \((0, \pi / 2],\) and sketch the graph of the inverse function.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and 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.