Convert $\frac{2 \pi}{3}$ radians to degrees.
Answer (2)
Identify the given angle in radians: 3 2 π .
Apply the conversion factor: multiply the angle in radians by π 180 to convert to degrees.
Simplify the expression: 3 2 π × π 180 = 3 2 × 180 .
Calculate the final answer: 120 degrees.
Explanation
Problem Analysis We are given an angle in radians, 3 2 π , 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 that π radians is equal to 180 degrees. Therefore, 1 radian = π 180 degrees .
Calculation To convert 3 2 π radians to degrees, we multiply by the conversion factor: degrees = 3 2 π ⋅ π 180 We can simplify this expression by canceling out the π terms: degrees = 3 2 ⋅ 180 degrees = 2 ⋅ 3 180 degrees = 2 ⋅ 60 degrees = 120
Final Answer Therefore, 3 2 π radians is equal to 120 degrees.
Examples
Understanding radian to degree conversions is crucial in many fields, such as physics and engineering, where angles are frequently used in calculations. For example, when analyzing the trajectory of a projectile, you might need to convert the launch angle from radians to degrees to use trigonometric functions correctly. Similarly, in mechanical engineering, when designing rotating machinery, knowing the angular displacement in degrees helps in determining the position and velocity of different components. This conversion ensures accurate measurements and calculations in practical applications.
The angle 3 2 π radians converts to 120 degrees. This is achieved using the conversion factor of π 180 degrees per radian. The calculation simplifies to 120 degrees after simplification.
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