Unit Circle

S: professor dave explains (yay!)

Radius = 1 $r^2=x^2+y^2=1$

unit circle anki real real

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On the Hand Technique

OH MY GOD GETS KO NA YUNG HAND SIGNS

okay so, essentially, to find the upper right quadrant ng unit circle, it’s essentially like the coordinates $(x,y)$ is equal to $(\cos \theta ,\sin \theta )$.

now, the hand signs equate to that. for the left hand, each finger represents (from left to right) 90, 60, 45, 30, and 0 respectively. these are the “special triangles” and could be shortcutted by the counting the fingers in the left (for cosine) and right (for sine) respectively.

so count the fingers, root that, then over two, to get its cosine or sine value.

e.g. the cosine of $\frac{\pi }{6}$ or $30^{\circ }$ is $\frac{\sqrt{3}}{2})$ because there is 3 fingers to the left of the index finger. 3 is rooted, then divided by 2.

the sine is $\frac{1}{2}$ because there is only one finger to the right, and since $\sqrt{1}$ is just one, then it is simply $\frac{1}{2}$.

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For the Other Quadrants

just go down the x- or y-axis until you get to the point you are looking for.

it’s 0, 1/2, $\frac{\sqrt{2}}{2}$, $\frac{\sqrt{3}}{2}$, 1 respectively

he just said “once this is ingrained in you, you’ll never forget it, so just stare at this until it makes sense.” HE’S NOT WRONG THO.

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For Negative Points

go from point $(1,0)$ leading to $(0,-1)$, basically counterclockwise.