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If a snowboarder pulls off a 720∘720^\circ spin, they end up facing the exact same direction as someone standing completely still at 0∘0^\circ.
In geometry, angles were just the opening between two fixed lines, but in trigonometry, an angle represents an active rotation.

Angles in Standard Position

An angle is in standard position when its vertex sits at the origin (0,0)(0,0) and its starting ray, called the initial side, lies flat along the positive x-axis.
The ray that rotates into the final spot is called the terminal side, and the direction of rotation determines the sign of the angle.
Rotating counterclockwise produces a positive angle, while rotating clockwise produces a negative angle.
The convention of dividing a full circle into 360∘360^\circ dates back over 3,000 years to ancient Babylonian astronomers, who based it on their 360-day calendar year and base-60 counting system.
How do you accurately place any angle without a protractor?

Sketching Angles by Quadrant

To sketch an angle, track the coordinate axes as quarter-turn checkpoints: the positive y-axis is at 90∘90^\circ, the negative x-axis is at 180∘180^\circ, and the negative y-axis is at 270∘270^\circ.
Let's sketch θ=210∘\theta = 210^\circ. Since 210∘210^\circ is 30∘30^\circ past 180∘180^\circ, the terminal side lands firmly in Quadrant III.