Final answer:
To find the radian measure of a central angle, use the formula Θ = s / r with the arc length s and radius r, or convert from degrees to radians by multiplying by π/180.
Step-by-step explanation:
To find the radian measure of the central angle of a circle, you'll need to know either the arc length (s) or the degree measure of the angle. Since a full rotation of the circle is 360 degrees or 2π radians, you can use that relationship to convert between degrees and radians.
For a given arc length s and radius r, the central angle (Θ) in radians can be found using the formula Θ = s / r. This formula comes from the fact that the circumference of a circle is 2πr, so for a full revolution, the arc length is the same as the circumference, and the angle of rotation is 2π radians.
If you are given the degree measure of the central angle, you can convert it to radians by multiplying the degree measure by π/180. Conversely, to convert from radians to degrees, you multiply the radian measure by 180/π.