Easy way of memorizing values of sine, cosine, and tangent My math professor recently told us that she wanted us to be able to answer $\sin\left(\frac{\pi }{2}\right)$ in our head on the snap. I know I can simply memorize the table for the test by this Friday, but I may likely forget them after the test. So is there a trick or pattern you guys usually use to remember it? For example, SOHCAHTOA tells us what sine, cosine, and tangent really mean.

If not, I will just memorize the table. But just wanted to know what memorization techniques you guys use. I feel this is the perfect place to ask, because I bet a bunch of people in the math stackexchange, also had to go through the same thing freshman year of college.
Oh here is a picture of the unit circle:


First of all, you know the square diagonal is $\sqrt 2$ of the side, so sine and cosine of $45^\circ$ is $1/\sqrt 2 = \sqrt 2/2$ and tangent is $1$. 
Recall also the isosceles right triangle and find the described ratios in it
(see  https://commons.wikimedia.org/wiki/File:Reglas.svg)  
For the rest of the first quarter just memorize that the common 30-60-90 degree triangle has its shortest to longest edge ratio of $1:2$ (see the image linked above) so sine reaches $1/2$ at one-third of the right angle. And, from the other corner of the triangle, cosine of two-thirds of a right angle is $1/2$, too (since it is a ratio of the same two lengths).
Now, from the Pythagorean theorem, the third side is $\sqrt{1^2-(1/2)^2} = \sqrt 3/2$ of the hypotenuse, hence $\sin 60^\circ$ and $\cos 30^\circ$.
Finally tangent of $60^\circ$ is $\frac{\sqrt 3}2 : \frac 12 = \sqrt 3$ (tangent is an increasing function in the first quarter and $60^\circ > 45^\circ$, so $\tan 60^\circ > 1$) and tangent of $30^\circ$ is a reciprocal of it.
The last three rows of your table follow directly from the first row and from trigonometric functions' main properties — being even, odd and periodic. Just familiarize with their graphs and find specific points on them. Pay attention to different symmetries and translations between them.
