They meassure the X and Y when you moving a dial on a circle. Think of clock where the minute hand moves around: if you draw a line from where the minute hand points strairth down and straight left to project to axis, and where it hit the X and Y axis it meassure that length of the projected line.
Tan is just a ration of sin over cos, and it proves useful for a lot of triginomitry calculations.
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