/*! 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 11 Find the radian measure of the c... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 11

Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). (TABLE CAN NOT COPY)

Short Answer

Expert verified
The radian measure of the central angle can be found by dividing the arc length by the radius (\(Angle\, in\, Radian = \frac{Arc\, Length}{Radius}\)).

Step by step solution

01

Understand The Problem

To convert the arc length to the radian measure of the central angle, you need to use the formula: \(Angle\, in\, Radian = \frac{Arc\, Length}{Radius}\). This formula is derived from the relation \(s = r\theta\), where \(s\) is the length of arc, \(r\) is the radius of circle, and \(\theta\) is the angle in radian.
02

Substitute The Given Values

Substitute the given values of \(s\) (arc length) and \(r\) (radius) into the formula \(Angle\, in\, Radian = \frac{Arc\, Length}{Radius}\).
03

Calculate The Radian Measure

After substituting the given values into the formula, calculate the radian measure of the central angle. This involves dividing the given arc length by the given radius.

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

Determine the range of the following functions. Then give a viewing rectangle, or window, that shows two periods of the function's graph. a. \(f(x)=\sec \left(3 x+\frac{\pi}{2}\right)\) b. \(g(x)=3 \sec \pi\left(x+\frac{1}{2}\right)\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. After using the four-step procedure to graph \(y=-\cot \left(x+\frac{\pi}{4}\right),\) I checked my graph by verifying it was the graph of \(y=\cot x\) shifted left \(\frac{\pi}{4}\) unit and reflected about the \(x\) -axis.

In Exercises \(110-113,\) graph each pair of functions in the same viewing rectangle. Use your knowledge of the domain and range for the inverse trigonometric function to select an appropriate viewing rectangle. How is the graph of the second equation in each exercise related to the graph of the first equation? $$y=\sin ^{-1} x \text { and } y=\sin ^{-1} x+2$$

If \(f(x)=\sin x\) and \(f(a)=\frac{1}{4},\) find the value of \(f(a)+f(a+2 \pi)+f(a+4 \pi)+f(a+6 \pi)\).

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I made an error because the angle I drew in standard position exceeded a straight angle.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

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.