Math Is Fun Forum

Βεν Γ. Κυθισ

Member

Registered: 2018-10-09

Posts: 21

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:
[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:

---

Profile image background is from public domain.
1+1=|e^(π×i)-1|

Βεν Γ. Κυθισ

Member

Registered: 2018-10-09

Posts: 21

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).

---

Profile image background is from public domain.
1+1=|e^(π×i)-1|