13.3 Radian Measure A central angle of a circle is an angle with a vertex at the center of the circle. An intercepted arc is the portion of the circle with endpoints on the sides of the central angle and remaining points within the interior of the angle. When a central angle intercepts an arc that has the same length as a radius of a circle, the measure of the angle is defined to be 1 radian. r r 1 radian

Because the circumference of a circle is 2πr, there are 2π radians in any circle. Since 2π radians = 360 o and therefore π radians = 180 o you can use a proprotion such as (see below) tp convert between degrees & radians. EX 1: Find the radian measure of 60 o EX 2: Find the degree measure of 5π/2 radians.

degrees to radians radians to degrees RULES EX 3: Find the degree of EX 4: Find 27 o to radians

Radian version

arc length s = central angle measure θ circumference 2π 2π Property Length of an intercepted arc For a circle of radius r and a central angle of measure θ (in radians) the length "s" of the intercepted arc is s = rθ r r s θ 3 s b

Attachments