/*! 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 74 Find the length of the arc on a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 74

Find the length of the arc on a circle of radius \(r\) intercepted by a central angle \(\boldsymbol{\theta}\). Express arc length in terms of \(\pi .\) Then round your answer to two decimal places. (TABLE CAN NOT COPY)

Short Answer

Expert verified
The arc length \(s\) can be calculated by multiplying the radius \(r\) by the central angle \(\theta\), if expressed in radians. The result is in terms of \(\pi\) and should be rounded to two decimal places.

Step by step solution

01

Understand the Circle

Look at a circle with an angle \(\theta\) representing a segment. The proportion of that segment compared to the entire circle (360掳 or \(2\pi\) radians) is equal to the proportion of the length of that segment's arc (represented here as \(s\)) compared to the entire circumference.
02

Use Arc Length Formula

The formula for finding the arc length is \(s = r\theta\) where \(s\) is the arc length, \(r\) is the radius, and \(\theta\) is the central angle in radians. Apply this formula using the given \(r\) and \(\theta\).
03

Convert to Terms of Pi

To express this in terms of \(\pi\), remember that a full angle (360掳) is \(2\pi\). Therefore, when you plug in your central angle \(\theta\) into the arc length formula, you should ensure it is in radians or convert it if necessary to radians by dividing by 180 and multiplying by \(\pi\).
04

Round Your Answer

Calculate the value you get from applying the formula and convert this to decimal form. Then, round to two decimal places as per the exercise instructions.

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

What is a periodic function? Why are the sine and cosine functions periodic?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The sine and cosine are cofunctions and reciprocals of each other.

Find all zeros of \(f(x)=2 x^{3}-5 x^{2}+x+2\).

Define the sine of \(t\).

Exercises \(117-119\) will help you prepare for the material covered in the next section. In each exercise, complete the table of coordinates. Do not use a calculator. $$y=4 \sin \left(2 x-\frac{2 \pi}{3}\right)$$ $$\begin{array}{|c|c|c|c|c|c|} \hline \boldsymbol{X} & \frac{\pi}{3} & \frac{7 \pi}{12} & \frac{5 \pi}{6} & \frac{13 \pi}{12} & \frac{4 \pi}{3} \\ \hline \boldsymbol{y} & & & & & \\ \hline \end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

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.