7.1 Radian and Degree measure

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Presentation transcript:

7.1 Radian and Degree measure Objectives: • Changing Degrees to Radians • Changing Radians to Degrees

Concept: Definition of a Radian • Radian is the measure of the arc of a circle . • Unit circle is a circle with a radius of 1.

Concept: Definition of a Radian The circumference of a circle with a radius of “r” is 2πr. Therefore, a full rotation in radian measure is 2π. 360º = 2π 180º = π r

Concept: Things That Are Equal 360º = and 180º = So or

Concept: Converting R = D • where R = radians Degrees into Radians: R = D • where R = radians and D = degrees Note: You should leave your answer in terms of π. Ex: Convert 45º to radians R = 45º • = 45π = π 1 180 4

Concept: Converting Ex: Convert 210º degrees to radians. Answer 7π 6 You try: Ex: Convert 210º degrees to radians. Answer 7π 6

Concept: Converting D = R • where R = radians Radians to Degrees: D = R • where R = radians and D = degrees Note: In this case, the π usually disappears. If the radian was given to you as a decimal, then you will use 3.14… for π. Ex: Convert radians to degrees. D = 7π • = 1260π = 315º 4 4π

Concept: Converting Ex: Convert 3π radians to degrees. 8 Answer: 67.5º You try: Ex: Convert 3π radians to degrees. 8 Answer: 67.5º

HOMEWORK IXL A2:X.1