How to memorize the coordinates of the unit circle

One method to memorize the unit circle is to remember key angles in radians and their corresponding coordinates. For example,:

$ \text{At } \theta = 0, \ (1, 0) $

$ \text{At } \theta = \frac{\pi}{2}, \ (0, 1) $

$ \text{At } \theta = \pi, \ (-1, 0) $

$ \text{At } \theta = \frac{3\pi}{2}, \ (0, -1) $

$ \text{At } \theta = 2\pi, \ (1, 0) $

These points divide the unit circle into four quadrants.

Another way to memorize the unit circle is to use symmetry. Remember the coordinates for 0, frac{pi}{2}, pi, and frac{3pi}{2}, then reflect them in each quadrant:

$ (cos( heta), sin( heta)) $

For example, at heta = frac{pi}{6}, the coordinates are:

$ (frac{sqrt{3}}{2}, frac{1}{2}) $

Reflect these values in each quadrant to fill out the circle.

Use mnemonic devices to memorize key points on the unit circle. For example:

$ cos(0) = 1, sin(0) = 0 $

$ cos(frac{pi}{2}) = 0, sin(frac{pi}{2}) = 1 $

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