# 4.1 Radian and Degree measure

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

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

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
Use degree to rads. Use rads 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

where is measured in radians
Area of a Sector of a Circle where is measured in radians A sprinkler on a golf course fairway is set to spray water over a distance of 70 feet and rotates through an angle of 120 degrees. Find the area of the fairway watered by the sprinkler. 120o = how many radians? 70 ft 79-99 odd, 107

Tip of the second hand as it passes around the clock face.
Finding Linear Speed The second hand of a clock is 10.2 cm long. Find the linear speed of the Tip of the second hand as it passes around the clock face. Linear speed v Arc length s =1.068 cm/sec

Similar presentations