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Chapter 0: Problem 9

Convert each angle to degree measure. $$ \frac{\pi}{3} $$

Short Answer

Expert verified
The given angle is \(\frac{\pi}{3}\). To convert it to degrees, multiply by the conversion factor \(\frac{180^\circ}{\pi}\) and simplify: \(\frac{\pi}{3} \cdot \frac{180^\circ}{\pi} = \frac{180^\circ}{3} = 60^\circ\) So, \(\frac{\pi}{3}\) radians is equal to \(60^\circ\) degrees.

Step by step solution

01

Write down the given angle

We are given the angle as: \[\frac{\pi}{3}\]
02

Multiply by the conversion factor

Now, multiply the given angle by the conversion factor $$\frac{180^\circ}{\pi}$$. This will convert the value from radians to degrees. \[\frac{\pi}{3} \cdot \frac{180^\circ}{\pi}\]
03

Simplify

Upon cancelling the \(\pi\) terms and simplifying, we will obtain the angle in degrees. \[\frac{180^\circ}{3}\]
04

Calculate the degree measure

Finally, divide $$180^\circ$$ by 3 to get the degree measure of the given angle. \[60^\circ\] Thus, the angle $$\frac{\pi}{3}$$ radians is equal to $$60^\circ$$ degrees.

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