Chapter 6.1 ANGLES

FISRT!
Angles have two sides: the Initial Side and the Terminal Side. 

The rotation of the rays always starts on the intial side, and always ends on the terminal side.
Many angles can have the same initial and terminal sides. These are called Coterminal Angles.

When it is rotated counter-clockwise to the terminal side, the angle is positive. When it is rotated clockwise, the angle is negative.


Standard Position:
The vertex is on the origin of the graph, and the initial side is on the positive x-axis.

Finding Cotermianl Angles

is standard position, find two positive angles and two negative angles that are coterminal with

 to find positive coterminal angles, you can add any positive integer multiple of 360° to 

 to find negative coterminal angles, you can add any negative integer multiple  of 360° to

Radians


Definition: one radian is the measure of the central angle of a circle subtended by an arc equal in length to the radius of the circle.
The length of the radius is eqaul to the arc length.

Realtionships Between Degrees and Radians

1. 
2. 
3. 

Changing Angular Measures

Degrees to Radians: 

Radians to Degrees: 

Formula for the Length of a Circular Arc

If an arc of length s on a circle of radius r subtends a central angle or a radian measure θ, then s=rθ.

Formula for the Length of a Circular Sector

If θ is the radian measure of a central angle of a circle of radius r and if A is the area of the circular sector determined by θ, then A=1/2 r²θ.

-Austin A.K.A. the Hiphopopotamus