1. Radian Measure Advanced Geometry Circles Lesson 4

2. There are many real-world applications which can be solved more easily using an angle measure other than the degree. This other unit is called the radian.

3. How do Radians relate to Degrees? For a circle with a radius of 1 unit, In degrees, the measure of a full circle is 360°. So, π radians = 180°

4. Degree / Radian Conversions 1 radian = degrees1 degree = radians Angles expressed in radians are written in terms of . π radians = 180°

5. Examples: Change 115° to radian measure in terms of . Change radians to degree measure to the nearest hundredth. Change 5 radians to degree measure to the nearest hundredth.

6. Arc Length length of a circular arc central angle θ must be measured in radians.

7. Examples: Given a central angle of, find the length of its intercepted arc in a circle of radius 3 inches. Round to the nearest hundredth.

8. Examples: Given a central angle of 125°, find the length of its intercepted arc in a circle of diameter 14 centimeters. Round to the nearest hundredth.

9. Examples: An arc is 14.2 centimeters long and is intercepted by an central angle of 60°. What is the radius of the circle to the nearest hundredth?

10. Sector of a Circle Definition – a region bounded by a central angle and the intercepted arc

11. Area of a Sector r θ must be measured in radians.

12. Find the probability that a point chosen at random lies in the yellow shaded area. Example: Find the total area of the yellow sector to the nearest hundredth.