On a unit circle (circle with radius 1 and the center at the origin) draw a line from the origin with your desired angle (wrt to the x-axis) as slope. cos is the x component of the point where the line crosses the circle. sin is the y component of the point where the line crosses the circle. tan is the y component of the line when the x component is 1 or -1. the vertical line at 1 or -1 is the tangent of the unit circle with respect to the x-axis.
EDIT: here is a [picture](https://i.imgur.com/U1NTgzA.png). note, tan in the picture uses a slightly different (but equivalent) definition. also [cool video](https://youtu.be/h9CRR_07eAI) from below
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