2D vector math hero - polar movement

Vector math for polar movement in 2D games (Unity)

Polar movement, i.e. moving objects at an angle, is something that people starting out in games programming often have trouble with. Coordinate systems are easy to understand, and so is moving things left and right or up and down; but what if you want to move at angles that are not parallel to an axis, like 30° upwards, or towards a target? How do you get a vector that represents that direction of movement?

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