 Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2019-04-16 14:19:20

Βεν Γ. Κυθισ
Member Registered: 2018-10-09
Posts: 20

### Altitude Trigonometric Functions?

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:

After those steps have been done, calculate the trigonometric functions for ΔPAF at ∠P.
You should get something that looks like this:  (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:

1+1=|e^(π×i)-1|

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## #2 2019-04-16 14:22:36

Βεν Γ. Κυθισ
Member Registered: 2018-10-09
Posts: 20

### Re: Altitude Trigonometric Functions?

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).

1+1=|e^(π×i)-1|

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