Degrees
What is $\sin 0^{\circ}$?
\[0\]
What is $\sin 30^{\circ}$?
\[\frac{1}{2}\]
What is $\sin 45^{\circ}$?
\[\frac{\sqrt{2}}{2}\]
What is $\sin 60^{\circ}$?
\[\frac{\sqrt{3}}{2}\]
What is $\sin 90^{\circ}$?
\[1\]
What is $\cos 0^{\circ}$?
\[1\]
What is $\cos 30^{\circ}$?
\[\frac{\sqrt{3}}{2}\]
What is $\cos 45^{\circ}$?
\[\frac{\sqrt{2}}{2}\]
What is $\cos 60^{\circ}$?
\[\frac{1}{2}\]
What is $\cos 90^{\circ}$?
\[0\]
What is $\tan 0^{\circ}$?
\[0\]
What is $\tan 30^{\circ}$?
\[\frac{\sqrt{3}}{3}\]
What is $\tan 45^{\circ}$?
\[1\]
What is $\tan 60^{\circ}$?
\[\sqrt{3}\]
What is $\tan 90^{\circ}$?
\[\text{undefined}\]
For what values are $\sin$ and $\cos$ the same?
\[45^{\circ}\]
Which $\sin$ and $\cos$ values swap over?
\[30^{\circ}, 60^{\circ}\]
What is special about the value under the square root for sine $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$?
What is special about the value under the square root for cosine $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$?
Radians
What is $\sin 0$?
\[0\]
What is $\sin \frac{\pi}{6}$?
\[\frac{1}{2}\]
What is $\sin \frac{\pi}{4}$?
\[\frac{\sqrt{2}}{2}\]
What is $\sin \frac{\pi}{3}$?
\[\frac{\sqrt{3}}{2}\]
What is $\sin \frac{\pi}{2}$?
\[1\]
What is $\cos 0$?
\[1\]
What is $\cos \frac{\pi}{6}$?
\[\frac{\sqrt{3}}{2}\]
What is $\cos \frac{\pi}{4}$?
\[\frac{\sqrt{2}}{2}\]
What is $\cos \frac{\pi}{3}$?
\[\frac{1}{2}\]
What is $\cos \frac{\pi}{2}$?
\[0\]
What is $\tan 0$?
\[0\]
What is $\tan \frac{\pi}{6}$?
\[\frac{\sqrt{3}}{3}\]
What is $\tan \frac{\pi}{4}$?
\[1\]
What is $\tan \frac{\pi}{3}$?
\[\sqrt{3}\]
What is $\tan \frac{\pi}{2}$?
\[\text{undefined}\]
What is special about the value under the square root for sine $\frac{\pi}{6}$, $\frac{\pi}{4}$ and $\frac{\pi}{3}$?
What is special about the value under the square root for cosine $\frac{\pi}{6}$, $\frac{\pi}{4}$ and $\frac{\pi}{3}$?
Periodicity and symmetry
After how many radians does $\sin$ repeat?
\[2\pi\]
What’s another way of stating that $\sin$ repeats every $2\pi$ radians?
\[\sin(\theta) = \sin(\theta + 2\pi)\]
After how many radians does $\cos$ repeat?
\[2\pi\]
What’s another way of stating that $\cos$ repeats every $2\pi$ radians?
\[\cos(\theta) = \cos(\theta + 2\pi)\]
After how many radians does $\tan$ repeat?
\[\pi\]
What’s another way of stating that $\tan$ repeats every $\pi$ radians?
\[\tan(\theta) = \tan(\theta + \pi)\]
Because $\sin$ is the same going up as it comes down, what relation in radians can you write?
\[\sin(x) = \sin(\pi - x)\]
General Rules
What’s another way of writing $\sin(-\theta)$?
\[-\sin(\theta)\]
What’s another way of writing $-\sin(\theta)$?
\[\sin(-\theta)\]
What’s another way of writing $\cos(-\theta)$?
\[\cos(\theta)\]
Exact values at pi over twelve
What’s
\[\sin\left(\frac{\pi}{12}\right)\]
?
\[\frac{\sqrt{6} - \sqrt{2}}{4}\]
What’s
\[\cos\left(\frac{\pi}{12}\right)\]
?
\[\frac{1 + \sqrt{3}}{2\sqrt{2}}\]
What’s
\[\tan\left(\frac{\pi}{12}\right)\]
?
\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1}\]