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**Βεν Γ. Κυθισ****Member**- Registered: 2018-10-09
- Posts: 21

So, I was browsing Wikipedia and came across the Right Triangle article's Altitude section.

Then I noticed that the altitude line splits the right triangle into two other right triangles.

Then I thought, "I wonder what would happen if I calculated the trig functions for one of these little triangles…"

So I came up with these steps:

[list=*]

[*]Take a triangle ΔPAB where ∠A=90°, ∠P=θ, and line PB has length 1; then find the altitude and call it line f.[/*]

[*]Mark the point where the altitude meets the hypotenuse as point F.[/*]

[*]Take the new triangle ΔPAF and name line PA line b as it is the base of the triangle, and name line PF line e.[/*]

[*]Take the other new triangle ΔBAF and name line BA line a, and name the line BF line d.[/*]

[/list]

After those steps have been done, calculate the trigonometric functions for ΔPAF at ∠P.

You should get something that looks like this: https://www.desmos.com/calculator/j5wuwvtvk6 (the last three variables are capitalized because I had to capitalize E and I wanted it to be consistent).

For now I'm going to call these:

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1+1=|e^(π×i)-1|

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**Βεν Γ. Κυθισ****Member**- Registered: 2018-10-09
- Posts: 21

Also, if you make the hypotenuse have length √2, something interesting will happen to the graphs of these functions (you can do this by multiplying a and b by √2).

Profile image background is from public domain.

1+1=|e^(π×i)-1|

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