Radian measure
ratio of the length of an arc intercepted by a central angle and the radius of the circle
Radian measure is a unit that is used to measure the angles in a circle. In the radian measure, an angle is measured as the length of an arc divided by the radius. In other words, it is the ratio of the length of the arc of the circle to the radius of the same circle.
The radian measure is based on the assumption that the circumference of a circle is 2πr. This means that if we divide the circumference of a circle by its diameter, we get the value of π. In terms of radian measure, an angle of one radian is equivalent to an angle that subtends an arc on the circumference of the circle, which is equal in length to the radius of the same circle.
Hence, an angle of 2π radians is equal to a full circle of 360 degrees. Similarly, an angle of π/2 radians is equal to a quarter of a circle or 90 degrees. The relationship between the radian measure and the degree measure is given by the formula
θ(degrees) = θ(radians) x (180/π)
Where θ(degrees) is the angle in degree measure and θ(radians) is the angle in radian measure.
Radian measure is widely used in many areas of mathematics and physics, particularly in calculus, trigonometry, and other applications that deal with angles and circular motion.
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