Trigonometry help?

Radians are a way of measuring angles.

A full circumference is 360°. In radians, this is 2π.

(So π radians = 180°)

But why 2π? Because the circumference of unit circle (circle with r = 1) = 2πr = 2π

But why use circumference of unit circle?

In trig we often deal with the unit circle, and in that case, the radian measure of the angle just happens to be the same as the length of the arc with the same central angle.

And for other circles with radius r, then arc length is just the central angle (in radians) multiplied by r.

s = arc length

s = rθ (in unit circle where r = 1, then s = θ)

In trigonometry, angles are measured in a counter-clockwise direction starting at positive x-axis (this is called standard position). Sometimes an angle is said to be in a clockwise direction from positive x-axis. In that case, the angle has a negative value. An angle has 2 arms (or sides). The positive x-axis is the initial arm, while the other arm is called the terminal arm (or terminal side).

https://www.mathopenref.com/trigterminalside.html

Two angles are said to be coterminal if their terminal sides are in the same location.

For example, if one angle is 1/4 of a rotation (90° or π/2 radians) about the circle (starting at positive x-axis) and another angle is 1 1/4 rotation (450° or 5π/2 radians), then their terminal arms will both be located along positive y-axis. These angles are said to be coterminal.

https://www.mathopenref.com/coterminal.html