4.1 Radian and Degree measure Changing Degrees to Radians Linear speed Angular speed.

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4.1 Radian and Degree measure

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Presentation transcript:

4.1 Radian and Degree measure Changing Degrees to Radians Linear speed Angular speed

Definition of an angle An angle is made from two rays with a common initial point. In standard position the initial side is on the x axis

Positive angle vs. Negative angle Positive angles are Counter clockwise C.C.W. Negative angles are ClockwiseC.W.

Angles with the same initial side and terminal side are coterminal.

The measure of an angle is from initial side to terminal side Vertex at the origin (Center)

Definition of a Radian Radian is the measure of the arc of a unit circle. Unit circle is a circle with a radius of 1.

The quadrants in terms of Radians What is the circumference of a circle with radius 1?

The quadrants in terms of Radians What is the circumference of a circle with radius 1?

The quadrants in terms of Radians The circumference can be cut into parts.

The quadrants in terms of Radians The circumference can be cut into parts.

Find the Coterminal Angle Since equals 0. it can be added or subtracted from any angle to find a coterminal angle. Given

Radian vs. Degree measurements 360º = 180º = So or

Radian vs. Degree measurements 360º = 180º = So or To convert Degrees into Radians multiply by To convert Radians into Degrees multiply by

Change 140º to Radians Change to degrees Usedegree to rads. Userads to degrees

How to use radian to find Arc length The geometry way was to find the circumference of the circle and multiply by the fraction. Central angle 360º In degrees Are length called S would be

How to use radian to find Arc length In degrees Are length called S would be In radian the equation is

r = 9, θ = 215ºChanging to rads Are length S

Linear speed and Angular speed Linear speed is Angular speed is Assuming “constant speed”

Homework Page 269 – 272 #9, 12, 17, 23, 25, 31, 37, 40, 47, 57, 62, 67, 71, 75, 79, 83, 87, 91, 99, 102

Homework Page 269 – 272 #11, 15, 19, 24, 27, 35, 39, 43, 55, 59, 65, 70, 73, 77, 81, 85, 89, 93, 100, 108