/*! 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 46 Use an inverse trigonometric fun... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 46

Use an inverse trigonometric function to write \(\theta\) as a function of \(x .\)

Short Answer

Expert verified
The angle \(\theta\) can be expressed as a function of \(x\) using an inverse trigonometric function, for example: \(\theta = \sin^{-1}(x)\). Note that this solution is valid provided that \(x\) lies in the interval \([-1,1]\).

Step by step solution

01

Understand the Problem

The task is asking to write \(\theta\) as a function of \(x\) using an inverse trigonometric function. This means that the answer will look like this: \(\theta = \) inverse trigonometric function \((x)\). The inverse trigonometric functions include: \(\sin^{-1}(x)\), \(\cos^{-1}(x)\), and \(\tan^{-1}(x)\). Depending on the context of the problem or any additional information given, any of these functions may be used.
02

Use an Inverse Trigonometric Function to Express \(\theta\)

Following from step 1, if there's no other context involved, any inverse trigonometric function can be used to solve for \(\theta\). Let's use the arc sine function (\(\sin^{-1}\)) as an example. From the definition of the arc sine function, the angle \(\theta\) can be written as: \(\theta = \sin^{-1}(x)\).
03

Interpret the Solution

The result \(\theta = \sin^{-1}(x)\) indicates that \(\theta\) is the angle whose sine is \(x\). It is important to note that \(\sin^{-1}(x)\) returns an angle in the interval \(\[-\frac\pi2, \frac\pi2]\). Hence, this result is valid provided that \(x\) lies in the interval \([-1,1]\), because the sine function only takes values in this interval.

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

Use the properties of inverse trigonometric functions to evaluate the expression. \(\arccos \left(\cos \frac{7 \pi}{2}\right)\)

Fill in the blank. If not possible, state the reason. As \(x \rightarrow 1^{-},\) the value of \(\arccos x \rightarrow\) ___.

Evaluate the expression without using a calculator. \(\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\)

Use a calculator to evaluate the expression. Round your result to two decimal places. \(\arccos (-0.41)\)

Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle, as demonstrated in Example \(7.)\) \(\sec [\arcsin (x-1)]\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Pure Maths

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.