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Chapter 4: Problem 72

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 \(s\) of the circle, given the radius \(r\) and the central angle \(\theta\) (in degrees, which then gets converted to radians), will be the solution to \(s = r \cdot \(\theta_{\text{radians}}\)\). The final answer is expressed in terms of \(\pi\) and rounded to two decimal places.

Step by step solution

01

Understanding the given

In the provided problem, we need to find the length of the arc. Given are the radius of the circle, denoted by the variable \(r\), and the central angle, \(\theta\). Remember, in order to apply the formula for calculation of the arc length, the central angle should be in radians and not in degrees.
02

Converting central angle to radians

Before using the arc length formula, ensure the central angle, \(\theta\), is converted to radians if it is provided in degrees - this is done by using the conversion factor of \( \pi/180 \). So \(\theta_{\text{radians}} = \theta_{\text{degrees}} \times (\pi/180)\).
03

Applying the arc length formula

With the radius and angle (in radians), the arc length, \(s\), can now be calculated using the formula \(s = r \cdot \theta_{\text{radians}}\).
04

Expressing in terms of \(\pi\)

Express the result in terms of \(\pi\) wherever possible, as requested by the exercise.
05

Rounding to two decimal places

The final answer would be made precise by rounding to two decimal places.

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