Want to know how the English speakers teach maths? Just as the following:
Definition of an Angle
An angle is generated by rotating a ray about its fixed endpoint from an initial position
to a terminal position.
The initial position is called the initial side of the angle, the terminal position is called
the terminal side and the fixed endpoint is the vertex. The angle itself is the amount of
rotation from the initial side to the terminal side.
If the rotation of the terminal side from the initial side is counterclockwise, the angle
is defined as positive.
If the rotation of the terminal side from the initial side is clockwise, the angle is
defined as negative
Degrees
One complete rotation is defined as 360° .
Which means that 1° is defined as 1/360 of a complete rotation
We can break degrees down into smaller units in two ways:
1. Using decimals – Examples: 14.6° , 74.85° , 30.006°
2. Using Minutes and Seconds
1° = 60 minutes = 60'
1' = 60 seconds = 60"
Which means 1° = 3600 "
Examples: 83°47' , 63°58'30" , 23°19'44".
Definition of Coterminal Angles
Two angles that have the same initial and terminal sides are called coterminal angles.
Example 1: State a positive and a negative angle that is a coterminal angle to 120° .
Answer: 120° + 360° = 480° is coterminal to 120° .
120° − 360° = −240° is coterminal to 120° .
Example 2: State a positive and a negative angle that is a coterminal angle to − 80° .
Answer: − 80° + 360° = 280° is coterminal to − 80° .
− 80° − 360° = −440° is coterminal to − 80° .
