So in other words, this input is twice as big as this area.
black pen red pen, yay
okay in this video we will compare the traditional trig functions
and the hyperbolic trig functions
I know some of you guys might not have seen this yet, thats okay because
I will first review the traditional ones with you guys and
then we will see the connection between the traditional ones
and the hyperbolic ones, so be sure
you watch the whole video so that's how you can see the connection
and thats how you can get the enjoyment of learning mathematics
and before we start I just wanted to thank brilliant.org
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alright, so
traditional trig functions, its based on the unit circle
and the equation for the unit circle is
x^2+y^2=1
and we know, well, if we pick a point on the unit circle
let me just put it right here for example
and one of the things we can do is we can
first just kinda measure the angle
from the positive x-axis
to this point right here so you have to see
how big this angle is
And I will just call this angle to be t
And once we have this angle we know that
the x-coordinate of this point is just cos(t)
and the y value is just sin(t)
You might be wondering why don't I use theta?
You'll see why
Anyway, so this is pretty much it
And because this right here is the x value and this right here is the y value
If you plug this in
You automatically have that identity
cos²(t) + sin²(t) = 1 isn't it?
Right? x² plus y² is equal to 1 That's pretty much it
So that's it, that's good, alright?
Now!
For the hyperbolic ones
Instead of using a circle
We'll just be using a hyperbola