Okay. In this video I'm going to talk about the Unit Circle,
and this will be useful for all the trig stuff,
and I'm not going to talk about measuring angles or anything like that.
I'm just... if you've seen some of the trick stuff, just the trick to remember the values on the Unit Circle, so
remember that the circumference of a circle is 2πr
Well, the Unit Circle has radius 1, so remember that
the distance around the circle we measure the angles
from the X-axis counter-clockwise; the distance around is 2π.
So at the positive X-axis this will correspond to the angle of π.
And we know the angle of π, the values on the Unit Circle are (-1,0).
Well halfway will be π/2
Okay... In between π/2 and the angle 0,
so that'll just dissect the first quadrant into two equal pieces
that'll be the angle π/4.
And then we have an angle even small than that usually they want you to memorize
this will be π/6.
And then we have another angle up here... this will correspond to the angle π/3.
Okay, so again...
The angles hit the Unit Circle in different places and I'm just going to show you a trick
to remember the values on the Unit Circle.
Okay so this at least is a way that I seem to remember it.
So, you know the angle that goes...the (X,Y) coordinate that goes with 0
is easy to remember because it's on the X-axis so it's (1,0).
Likewise, the values that go with π/2 are easy to remember because
well that's on the Y-axis,
but people always forget the values that go with π/3, π/4, and π/6.
An easy way to remember it is...okay just make a little set of parenthesis.
Okay so there's my parenthesis...
Everywhere I'm going to make a fraction and I'm going to make the denominator 2.
So, I'm going to make a denominator of 2 everywhere.
And then what I do is, I write the numbers 1, 2, 3 down the the top left side,
and then I write 1, 2, 3 on the top going up on the right side.
So, here's my values... 1, 2, 3...
Do it on the same side... 1, 2, 3.
And now the last thing you need to remember is simply to take the square roots of the top part.
Okay so the last thing we do is take square roots,
so √1 is just 1
and then we get the √3, the √2/√2
the √3. Again, the √1 is just 1, so we don't write the square root we just leave it off.
And now you've got all of the values on the Unit Circle that go with the angles π/6, π/4, and π/3.
Okay so again the basic idea is just the little pattern.
Again notice the numbers in the denominator get smaller... 6, 4, 3, 2.
To get the actual (X,Y) coordinates, again you just make a fraction making the denominators 2's.
Put 1, 2, 3 down the top of the left side. 1, 2, 3 going up on the top of the right side.
Take the square roots of everything
and now you have the (X,Y) coordinates. So it says the angle of π/3 is going to hit the Unit Circle
at the (1/2,√3/2), etc.
And now you can use these angles to find the other angles on the Unit Circle
and I actually talk about that a little more in-depth.
So, just a useful little trick a student of mine suggested posting this out there. She thought it was great
because she said she never could remember them and now she remembers them.
So, again nothing super fancy but hopefully just a little trick to help you remember
at least the (X,Y) coordinates on the Unit Circle in the first quadrant, and that's it. Alright good luck you all.