This is a great, very easy technique for remembering the values of the sine and cosine of any angle on the unit circle.
All you have to remember is: $0, 1, 2, 3, \text{ and } 4$ and $\frac{\sqrt{x}}{2}$.
Credit and gratitude for this technique must be given to Eli Hibit ([@pwnphysics](https://twitter.com/pwnphysics)), who described it on his podcast, [PWN Physics](http://t.co/NPRzrTzIfD).
Beginning in Quadrant I with angle $\angle \theta = 0$, all you have to do is remember to replace $x$ in $\frac{\sqrt{x}}{2}$ with $0, 1, 2, 3, \text{ or } 4$:
| Number | $\text{Value of } \theta$ | $\sin(\theta)$ | Actual Value of $\sin$ |
|---|---|---|---|
| 0: | $0$ | $\sin(0) = \frac{\sqrt{\color{red}0}}{2}$ | $0$ |
| 1: | $\frac{\pi}{6}$ / $30\circ$ | $\sin(\frac{\pi}{6}) = \frac{\sqrt{\color{red}1}}{2} = \frac{1}{2}$ | $\frac{1}{2}$ |
| 2: | $\frac{\pi}{4}$ / $45\circ$ | $\sin(\frac{\pi}{4}) = \frac{\sqrt{\color{red}2}}{2}$ | $\frac{\sqrt{2}}{2}$ |
| 3: | $\frac{\pi}{3}$ / $60\circ$ | $\sin(\frac{\pi}{3}) = \frac{\sqrt{\color{red}3}}{2}$ | $\frac{\sqrt{3}}{2}$ |
| 4: | $\frac{\pi}{2}$ / $90\circ$ | $\sin(\frac{\pi}{2}) = \frac{\sqrt{\color{red}4}}{2} = \frac{2}{2} = 1$ | $1$ |
For Quadrant II, the values count back down from $\frac{\sqrt{4}}{2}$ to $\frac{\sqrt{0}}{2}:$
| Number | $\text{Value of } \theta$ | $\sin(\theta)$ | Actual Value of $\sin$ |
|---|---|---|---|
| 4: | $\frac{\pi}{2}$ / $90\circ$ | $\sin(\frac{\pi}{2}) = \frac{\sqrt{\color{red}4}}{2} = \frac{2}{2} = 1$ | $1$ |
| 3: | $\frac{2\pi}{3} (= \frac{4\pi}{6})$ / $120\circ$ | $\sin(\frac{\pi}{3}) = \frac{\sqrt{\color{red}3}}{2}$ | $\frac{\sqrt{3}}{2}$ |
| 2: | $\frac{\pi}{4}$ / $45\circ$ | $\sin(\frac{\pi}{4}) = \frac{\sqrt{\color{red}2}}{2}$ | $\frac{\sqrt{2}}{2}$ |
| 1: | $\frac{\pi}{6}$ / $30\circ$ | $\sin(\frac{\pi}{6}) = \frac{\sqrt{\color{red}1}}{2} = \frac{1}{2}$ | $\frac{1}{2}$ |
| 0: | $\frac{2\pi}{2} (= \pi)$ / $180\circ$ | $\sin(\pi) = \frac{\sqrt{\color{red}0}}{2} = 0$ | $1$ |
In [ ]: