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:
Note the pattern:

$$\sin 0^{\circ} = \frac{\sqrt{0}}{2}$$
$$\sin 30^{\circ} = \frac{\sqrt{1}}{2}$$
$$\sin 45^{\circ} = \frac{\sqrt{2}}{2}$$
$$\sin 60^{\circ} = \frac{\sqrt{3}}{2}$$
$$\sin 90^{\circ} = \frac{\sqrt{4}}{2}$$

This is something of a mathematical coincidence as far as I know, so don't try to extend this to other angles; and it goes backwards for $\cos$.  Once you have these, you can find the other angles you want by drawing them on the unit circle and figuring out whether the values should be positive or negative, whether they should be $0$ or $1$, or otherwise whether they are "small" ($\frac{1}{2}$), "medium" ($\frac{\sqrt{2}}{2}$) or "large" ($\frac{\sqrt{3}}{2}$).
Consider the simple example first and then you can derive further values from it. Lets begin with the following table. Sin Cos Tan Table

All you need to remember about this table is the arrangement of rows and columns i.e. angles are placed in columns and trigonometric functions at the rows. So draw a table and start with the sine values. 

Step 1 (red): In each of the empty cells for sine of 0,30,45,60 and 90 write (0,1,2,3,4) respectively. 

Step 2 (green): Then divide each of them with 4 (i.e. 0/4, 1/4, 2/4, 3/4, 4/4). 

Step 3(blue): The next step is to take square root of each (i.e. sqrt(0/4), sqrt(1/4), sqrt(2/4), sqrt(3/4), sqrt (4/4)). 

Step 4(brown): Now cancel any terms from numerator and denominator if applicable and simplify the results. You end up with the values of sine 0,30,45,60 and 90. 

Drawing Sin Cos Tan Table

Step 5(orange):Once you have values for sine function, invert them for cosine i.e( sin 90 = cos 0, sin 60 = cos 30, sin 45 = cos 45 and so on) and you get values for cosine function. 

Step 6: For tangent, put sin/cos values and simplify. 

Step 7: You can extend the table for further angles by using formulas such as 


  sin(π−x)=sinx  sin⁡(π−x)=sin⁡x  and sin(π/2−x)=cosx sin⁡(π/2−x)=cos⁡x,
  and cos(π/2−x)=sinx cos⁡(π/2−x)=sin⁡x,