4 1 Radian and Degree measure Definition of

4. 1 Radian and Degree measure

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 is the measure of the arc of a unit circle. Unit circle is a circle with a radius of 1. https: //www. youtube. com/watch? v=Hh. Hds http: //www. youtube. com/watch? v=7 Qhg. YX 8 c. RE 4 QAM_Rc

Radian Protractor Worksheet • Materials – Worksheet – Circle with radius – String – Scissors Complete steps 1 -5

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. We’ll start by cutting it into fourths.

The quadrants in terms of Radians

• Complete steps 6 -8, fill in the blanks • Then starting with a fresh circle on the back of your original circle, write in the radian measurements

• Draw a fresh circle in your notes and practice using the patterns of 4 ths and 6 ths.

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

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

How to use radian to find Arc length In degrees Arc length called S would be Rewrite the equation replacing 360 degrees with it’s equivalent in radians, then simplify to find the new equation for arc length

Find the arc length in radians r = 9, θ = 50º Changing to rads Arc length S

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

Linear speed and Angular speed Linear speed is how fast a particle moves along a circular arc. Angular speed, is how fast the angle changes.

• How do we calculate how fast we are driving? • mi/hr or the distance divided by the time • The same idea applies to linear and angular speed

Linear speed and Angular speed Linear speed, v = Angular speed, Lower case “Omega” Assuming “constant speed”

A Ferris wheel has a 50 ft radius and makes 1. 5 revolutions per minute. What is the linear and angular speed in radians?

H Dub • 4 -1 Pg. 290 #1 -10, 15 -18, 21, 22, 55 -70, and 103