Presentation on theme: "4.1 Radian and Degree measure"— Presentation transcript:

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 Clockwise C.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.

What is the circumference of a circle with radius 1?

What is the circumference of a circle with radius 1?

The circumference can be cut into parts.

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

Complementary Angles – two angles are complementary
if their sum is 90 degrees or Supplementary Angles have a sum of 180 degrees or Find the complementary and supplementary angles for

360º = 180º = So or

360º = 180º = So or To convert Degrees into Radians multiply by To convert Radians into Degrees multiply by

To convert degrees to radians, multiply by To convert radians to degrees, multiply by Converting an angle from to decimal form.

Change 140º to Radians Change 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 = 215º Changing to rads Are length S

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

Consider a particle moving at a constant speed along a circular arc of
Linear and Angular Speeds Consider a particle moving at a constant speed along a circular arc of radius r. If s is the length of the arc traveled in time t, then the linear speed v of the particle is Linear speed v Moreover, if is the angle (in radian measure) corresponding to the arc length s, then the angular speed (the lowercase Greek letter omega) of the particle is Angular speed A relationship between linear speed and angular speed is