Radian Measure Advanced Geometry Circles Lesson 4.

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Presentation transcript:

Radian Measure Advanced Geometry Circles Lesson 4

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.

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°

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

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.

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

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.

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.

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?

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

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

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.