Convert [tex]$\frac{\pi}{3}$[/tex] radians to degrees.

We are given an angle in radians: 3 π ​ .
We use the conversion factor: 1 radian = π 180 ​ degrees .
We multiply the given angle by the conversion factor: 3 π ​ × π 180 ​ .
We simplify the expression to find the angle in degrees: 60 ​ .

Explanation

Problem Analysis We are given an angle in radians, 3 π ​ radians, and we want to convert it to degrees. To do this, we'll use the conversion factor between radians and degrees.

Conversion Factor The conversion factor is: 1 radian = π 180 ​ degrees . This means that to convert radians to degrees, we multiply the number of radians by π 180 ​ .

Applying the Conversion Now, we multiply the given angle in radians by the conversion factor: degrees = 3 π ​ ⋅ π 180 ​

Simplifying the Expression We can simplify this expression by canceling out the π terms: degrees = 3 1 ​ ⋅ 180 degrees = 3 180 ​ degrees = 60 So, 3 π ​ radians is equal to 60 degrees.

Final Answer Therefore, 3 π ​ radians is equal to 60 degrees.


Examples
Understanding radian to degree conversions is crucial in many fields, such as physics and engineering. For example, when analyzing the motion of a pendulum, you might measure its angular displacement in radians. To easily visualize or communicate this angle, you would convert it to degrees. Similarly, in computer graphics, angles are often manipulated in radians, but for display purposes, they might be converted to degrees for better human readability. This conversion allows for seamless integration of mathematical models with real-world applications and intuitive understanding.

Answered by GinnyAnswer | 2025-07-05

To convert 3 π ​ radians to degrees, we multiply it by the conversion factor π 180 ​ . Simplifying this gives us 60 degrees. Thus, 3 π ​ radians is equal to 60 degrees.
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Answered by Anonymous | 2025-07-06