If I had just one chance

amoroccidit-subsilentio asked: Can you tell me about the conceptual number of yours?

It’s a precal number. It’s used to solve for solutions outside of the unit circle (without stretching the circle itself). 

I’m just using Cos and sin and Cos graphs are easier so I started with Cosine. 

Cos(x) = A Where A > 1 or <-1. Because if it were between those, just use inverse.

Cos(x) = 2 for example.

You use the base formula, Cos(x) = N + (A - Cos(N))U

N is your angle out, or projection from the center. 

Cos(x) = 2pi + (2 - 1)U = 2pi + 1U

U stands for Unit outside of the unit circle. U is the number, I made.

Step 1 ^^ 

Step 2 is:

Finding: 1) Angle, 2) Distance/U, 3) Coordinates.

It’s just using polar coordinates to find those. 

You need to have the angle and U distance to find the coordinates or you need to have the coordinates to find the rest. 

If you have the coordinates, just use pythagorean to get the hypotenuse, since it’s a right triangle and the hypotenuse is U+1. Because U is outside the circle and 1 is the unit circle’s radius.

It’s kind of just used to make more problems using imaginary numbers. 

You can have any projections, and there are rules.

Quadrant I and IV angles follow the formula Cos(x) = N + (A - Cos(N))U

Quadrant II and III are same except Cos(x) = N + (A+Cos(N))U 

Different because the 2 & 3 are going to have a negative number anyways. 

Step 3 is the same as step one but it’s projection. I just made it part of step 1. 

You can also graph these on the Unit circle line thing. Normally, cos starts on (0,1) and just squiggles til -1. 

I made a graph formula for that too.

Y = (-pi/2)X^2 + A 

You have to manually graph it though, because calculators wouldn’t let me do it, since it doesn’t exist yet.

But you use that formula to graph and use your calculator to find the Intercept at 0. 

The number for X you get at the intercept is L, or Length.

There’s a little key I made.

At (0,A) you start.

(+-L, 0) X-intercept

(+-2L, -A) Next Vertex

(+-4L, A) Period.

It’s a system of using imaginary numbers in trig :]