Question

What is 720° converted to radians?
a) π
b) 2π
c) 4π
d) 6π

Answer 1

720° converted to radians is 4π, which corresponds to option c.

Step-by-step explanation:

The conversion from degrees to radians involves utilizing the relationship where 1 full revolution or circle in degrees is equivalent to 2π radians. Therefore, to convert 720° to radians, we employ the formula
`\( \text{Radians} = \frac{\text{Degrees} * π}{180}\).` Substituting 720 for degrees in the formula gives
`\( \text{Radians} = (720 * π)/(180) = 4π\)`. This means that 720° is equivalent to 4π radians, aligning with option c.

Understanding the conversion between degrees and radians is crucial in various mathematical applications, particularly in trigonometry and calculus. Radians are a unit of measurement used to express angles in terms of the radius of a circle, making calculations involving circular motion, periodic phenomena, and calculus operations more convenient. In this case, 720° represents two complete circles or revolutions, which equates to 4π radians, providing a more comprehensive understanding of angular measurement in radians.

Converting between degrees and radians aids in seamlessly interchanging angular measurements in different contexts. In the case of 720°, recognizing that a full revolution of 360° occurs twice, resulting in 2 x 2π = 4π radians, facilitates mathematical operations involving angles, trigonometric functions, and geometric calculations, allowing for precise and accurate representations of angles in various mathematical scenarios.