Aim: How do we define radians and develop the formula Do Now: 1. The radius of a circle is 1. Find, in terms of the circumference. 2. What units do we use for measuring a) length b) weight c) angle? HW: p.405 # 28,30,32,34,36,38,39,40,42,43

Another unit to measure angle is the radian Radian is the central angle that intercepts an arc whose length is the same as the radius.

If we choose a circle with a radius of 1, the circle is referred to as a unit circle. If the central angle of the unit circle intercepts an arc with length 1 then the measure of the central angle is 1 radian.

O  r = 1 1 radian Arc length = 1 The circle has radius equals 1. The central of the circle that intercepts the arc with length 1 is equal to 1 radian Use the same reason, if the radius is 2 units then the central angle equals 1 radian when the intercepted arc is also 2 units

One circle = 360° (degrees) One circle = 2π radians ----------------------------------- 1π radians = 180° 90  /2 radians 270  3/2 radians

The length of an arc can be found by using the formula, s=rθ, where: Arc Length The length of an arc can be found by using the formula, s=rθ, where: ‘s’ is the length of the arc. ‘ r ‘ is the radius of the circle. ‘θ ‘ is the radian measure of the central angle.

Examples: a) Find the length of an arc that subtends a central angle of 5π/6 in a circle with radius of 12 cm. s = rθ =12⋅5π/6 = 10π ≈ 31.42 cm b) Find the radius of a circle, if the arc length is 10 and the central angle equals 2 radians. 10 / 2 = 5 c) If the radius of a circle is 15, find the central angle when the arc length equals 45. 45/15 = 3 radians