4.1 Radian Measure

♥ The radian measure of  angle θ is defined as the length, a, of the arc that subtends the angle divided by the radius,r , of the circle : θ = a/r

♥ 2π rad = 360° or π rad = 180°.

♥ To convert degree measure to radian measure, multiply the degree measure by π/180° radians.

♥ To convert radian measure to degree measure, multiply the radian measure by (180/π)°.

Example 1 : Degree Measure to Radian Measure

How ? Convert a degree measure to a radian measure, multiply the degree measure by π/180° radians.

45° = 45 x π/180°

      = π/4 radians.

Determine the approximate radian measure by using calculator.

π/4 = 3.142/4

       = 0.7855 radians.

Example 2 : Radian Measure to Degree Measure
How? Convert radian measure to degree measure, multiply the radian measure by (180/π)°
π/6 = π/6 x (180/π)°
       = 30°