maths - week 1
another thing going on in my head for quite a while.
i get sin and cos mixed up if i'm not actively looking and thinking about it.
then i go back to soh cah toa
note: i have no idea what i'm talking about
<-- previous week - next week -->
pi and radians and degrees.
there is a unit circle. it has a radius of 1.
a unit vector. radius length, kinda rotates.. at least in this stuff i'm thinking.
when the vector points straight up, it is sin (90) or 1
when it points down, it is sin(270) or -1
the 90 is like the vector rotated anti-clockwise 90 degrees
180 degrees is pi radians. a whole unit circle is 2*pi circumference
then cosine.. cos..
sin is the y value!
wherever the vector is 'pointing', is an x and y co-ordinate
if it is pointing straight up, y is 1, the whole radius length, the vector length,
and the x value is 0, cos(90) is 0
before 45 degrees,
let's look at 30 degrees
the vector will be 'pointing' at x = cos(30), y = sin(30)
the vector is also the hypotenuse of a triangle. and remember it is length 1
sin is opposite over hypotenuse. the right angle is a vertical line from the point
meeting the x line (the line where y==0)
what? how? why? i'm confused, mang.
don't worry.. me too.
here we are supposed to think about how an equilateral triangle with side lengths 1 has three 60 degrees angles..
and if you chop it in half you get a triangle with a right angle, a 30 degree angle and a 60 degree angle
so the y value becomes a half.. 1/2
sin(30) == 1/2 or 0.5
a squared + b squared = 1 squared = 1
sin(30) .. 30 == opposite / hypotenuse and since hypotenuse is 1, just opposite = 1/2
bit of headache, but nearly.. cos is like sin's brother.. it's all good.
cos(30) = adjacent / hypotenuse =
a is the adjacent and c is the hypotenuse in:
a squared + b squared = c squared
we want to know the adjacent length..
so switch the formula..
a squared = c squared - b squared
adjacent squared == 1 - 1/2 squared = 1 - 1/4 = 3/4
adjacent == square root of (3/4) = square root of 3 / square root of 4
= (square root of 3) / 2
this is about 0.866
angle is 30.. x (horizontal) is root 3 over 2.. y (vertical) is 1/2.... (+0.866, +0.5)
60 degrees is like the flipside of 30 degrees
angle is 60.. x is 1/2.. y is root 3 over 2.... (+0.5, +0.866)
now 45 degrees means the other angle must be 45 degrees as there is the right angle too. and the side lengths, a and b, are equal.
if you have a unit square, all sides are 1, and cut it diagonally in half, the hypotenuse is the square root of (1 squared + 1 squared), or square root of 2
sine is opposite over hypotenuse..
1 / root 2
cosine is adjacent over hypotenuse..
1 / root 2
1 / root 2
what we do here is say root 2 / root 2 == 1
1 / root 2
root 2 * 1 == root 2
the root 2 * root 2 makes a 2
so it's (root 2) / 2
sin 45 is (square root of 2) / 2, and cos 45 is (square root of 2) / 2
x, y = 0.707, 0.707
maths for blondes lol
why not!
round and round.. what it is..
columns = list(zip(*matrix))
i'm not sure where i'm going with this.. what is a matrix?
0,0 origin .. [0 0] to 0,1.. [0 1] .. [0 0][0 1] ?