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There are 10 types of people in the world: those who know binary, and those who don't.

One easy way to remember the unit circle is to memorize the pattern in one quadrant, then use symmetry. So, sine goes 0/2, '1/2, '2/2, '3/2, '4/2 (where 'x is the square root of x) for 0, pi/6, pi/4, pi/3, pi/2 respectively. Of course, '1/2 is just 1/2, and '4/2 is just 1. I'm using the unsimplified version to make the pattern clear. And cos is just the opposite: it goes 4 3 2 1 0 (counterclockwise). Then, you can use sum/difference angle laws to fill in for whatever else you need. The other three quadrants are symmetrical, with sign changes as needed. So, you really only have to remember five things: the four "base" angles, and the fact that you divide the sine and cos by 2. Sorry if this is a bit messy, I'm typing it on my phone.

The unit circle keeps coming back, so it is definitely worth learning well.

I have already memorized the unit circle. It is really easy to remember. Plus I learned it last year which helps.

once when i was young i loved math but now it is like:
Omg noooooo Math so i said Well this is useless

Most people think math is useless (I used to), and it is to some degree. However, depending on your career path, your going to need to know a little more than 2+2=4. Right?

Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different.

Oh math gives me nightmares....

OMG I LOVE MATH!!!! I don't know what I would do without it :'(

However, depending on your career path, your going to need to know a little more than 2+2=4. Right?

You need to know basic math to get by. If you are not going into a math related field the highest math you would probably need is Algebra I.

Psychology: Stats.

You need Stats for Psychology? Why?

You need to know basic math to get by. If you are not going into a math related field the highest math you would probably need is Algebra I.

how will reading Shakespeare help us in our daily lives?

Okay, so the actual formula for the chi-squared test is pretty hard to write in AG, because it involves a lot a subscripts and special symbols. So, here is an image:


This gives you the chi squared value, which you then plug into a table based on the degrees of freedom, which depends on your sample.

This is the chart:


So, lets say you had a coin, and you wanted to know if it was a fair coin or not. You flip it 200 times, and get 120 heads and 80 tails. Not exactly 50-50, but could it be within the range of expected values?

Step one: pick the null hypothesis: in this case, that the coin IS fair. So we Expect there to be 100 heads and 100 tails.

Step two: determine the degrees of freedom: in this case there is ONE degree of freedom. The only variable is the number of either heads or tails, since if we know one, we can subtract from 200 to get the other.

Step three: plug everything in:
(120-100)^2/100 + (80-100)^2/100 = 8 (I did this in my head, it might be a little off)

When we plug that into the table, we find that the p value* is
between .01 and .001, so we REJECT the null hypothesis. This means that the coin is NOT fair. In the table, this is listed as "significant".

*The P value is the likelihood of rejecting a true null-hypothesis. So, it is less than 1 percent likely that this is a fair coin, which isn't very likely at all.

Problem: what if I rolled a die 90 times, and got no ones, twenty 2s, fifteen 3s, ten 4s, twenty-five 5s, and twenty 6s? Should we consider this die to be fair?

(hint-you should have to do very little calculating)

So, lets say you had a coin, and you wanted to know if it was a fair coin or not. You flip it 200 times, and get 120 heads and 80 tails. Not exactly 50-50, but could it be within the range of expected values?