Behold, the reference angle formula

what does it do?

>>8797495
Given any angle in radians for x, it returns that angle's reference angle in radians

>>8797501
How does it work? Why does that expression you posted encapsulate such behavior?

File: photo.jpg (116KB, 900x900px) Image search: [Google]

116KB, 900x900px

>implying π exists
>implying the cos function exists

File: Capture2.png (5KB, 357x187px) Image search: [Google]

5KB, 357x187px

>>8797502
Great Question.
The ArcCos(Cos()) Function is a trig function called by its inverse, Plotting this gives you a zig-zag or triangle-wave function that reaches its max of y=pi at x=pi over and over. To generalize it to awave that varies between -1 and +1 with unit period it can be shortened to (1/pi)(2*Sin^-1 (Sin (2pi x))), this is a wave that reaches a max of y=1 at x=1/4, 1 cycle at each integer.
This can be derived from recognizing that reference angles are generally linear, and behave like this triangle wave. If you tried to create a ref angle function, instinctively one may try modulo or something like that. Notice how reference angle changes as a given angle increases. From 0 degrees to 90, the reference follows exactly with the angle, but after 90, to 180, it decreases like -x, and same with 180 to 360. The triangle wave we have can be shifted with multiplication and shit to make it match the period of the reference angle exactly. multiplying it by 45 and adding 45 to make its peak at 90, and dividing it by 360 to stretch its horizontal scale out to 90 as well. It can be simplified down to the degree version (pic related). Multiply by pi / 180 to get the op, which is in radians.

This function is 100% correct and is never wrong but i cant prove it

These niggers wanted me to use quadrants and shit but Im like fuck that so Here is a formula

>>8797515
>Implying something imaginary could get us to the moon

File: fixed.png (5KB, 575x238px) Image search: [Google]

5KB, 575x238px

Actually, I'm retarded. This is the formula for radians. I forgot how conversion worked. This one is actually precise and works 100% of the time. The degrees one is correct, though.

>>8797437
why not just do (pi)x/180 to convert angles to rads? what purpose does the arccos(cos( serve is it just cancels out?

File: 1486568362316.jpg (18KB, 680x410px) Image search: [Google]

18KB, 680x410px

my formula is vastly superior

[eqn]\min\left(\theta, \pi-\theta\right)[/eqn]
Simpler and prettier

>>8799104
what is the sideways mars sign?

File: 1487475839483.png (13KB, 952x82px) Image search: [Google]

13KB, 952x82px

>>8799104
actually this is the best formula