Notes

An original function is f(x). An even function becomes the same as the original when it is flipped over the y-axis; i.e, f(x) = f(-x)
The property of odd functions is -f(x) = f(-x); after flipping over the x and y, you will get f(x) (origin symmetry. An odd function either passes through the origin (0, 0) or is reflected through the origin.)
Replacing x with a negative x is reflecting over the y axis. Whatever x value you input, it gives you the answer if you had made it negative; its changing the location in the y axis
A negative out in front is reflection over the x axis. Whatever f of a certain value is, it gives you negative instead; its changing the location in the x axis

Because sin is an odd function, you get sin(-x) = -sin(x)
To get the period subtract either the peaks or bottoms

cos(theta) is just sin(theta) shifted to the left by pi/2
The x intercepts for cos is all the odd multiplies of pi over 2. But you can't write it as npi / 2, because that accepts even multiplies. If n is 4, your result is just 2pi. Instead, it is written as npi + pi/2, which can be combined to pi(2n+1)/2. It multiplies with 2, then becomes odd by adding 1
Because cos is an even function, you get cos(-x) = cos(x)

In a tan function; when undefined you get a VA at the odd multiples of pi/2; if it's at the top or bottom middle, cos is 0
when evaluating sin/cos, don't do reference angle method; just use location in the unit circle.
x intercepts at multiplies of pi
because tan is not a wave, it doesn't have an amplittude.
Unlike the other two with period of 2pi, tan's period is just pi
Bcause tan is odd, we have the property: tan(-x) = -tan(x)

Rewatch for other three functions;
Their periods and symmetry are inherited from the function
Cos is sin shifted to the left by pi / 2
No x intercepts for sin and cos





Questions
- How is -1/8 * 4^x equal to -(1/8 * 4^x)
- How does -f(x) = f(-x) make sense, shouldn't it equal f(x) for an odd function
- if you do 3pi/2, that is at 0, -1. The reference angle is pi / 2. That gives you sqr4)/2. Its -1 because its not in quadrant 2. But what quadrant is it in?
- I don't get how the vertical line is sin(pi/2 + theta): https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:trig-id/v/trig-angle-rotations
- At 40:00 for calcualting the period what happens if you do -pi -pi? isn't that -2pi? Same thing so doesn't matter?
- At 43:00 he does 2npi + pi, then factors out pi and gets pi(2n + 1)? Where is the 1 from?
- See 64:00 he did something interesting

In a unit circle, hypotenuse and radius is one. So when you do sin(theta), or opposite / hyp, its really just opposite because hypotenuse is just one.
The unit circle is also a real line. pi / 2 is 90 degrees at 0, 1. Because sin is the y axis, sin is just 1 for pi / 2.
When you have a function like f(-x) = something, you have to change every x in the equation. -f(x) distributes to the equation. https://www.intmath.com/blog/mathematics/how-to-reflect-a-graph-through-the-x-axis-y-axis-or-origin-6255