How Sine and Cosine is related?

Question

I found a formula that says:

cos2+cosine2=1 (the 2s are squares)

How do you find that formula?
It was stated that the formula is related to the Pythagoras Theory. How come? Can someone explain?

Answer 1

I dont remember the proof of the top of my head, but what your asking is that

sin^2(x) + cos^2(x) = 1 rite?

If you want, I'll find that for you, but I'll send it to you in a like a day or 2 cause I'm doing that topic in an exam in a few weeks, but yeah, I think it does.... its called the Auxilory Method if i remember correctly, they use that to prove it.

Oh, by the way, by any chance, do you play maple story? (Stupid question i know, but I knew somebody named theresa that played maple).

Edit: Guys below me proved it I think xD, well thats that..

Answer 2

To represent the cosines and sinus,
you draw a circle of radius =1 The angle 0 (origin) is the horizontal line Ox originating from the center and oriented to the right. If you draw an angle the line representing the angle, will intersect the circle at the point M. the abscissa of M is cos x and the ordinate is sin x. Lets be O the center of the circle , projection of M on Ox = OA = cos x, and the length AM = sinx
in the triangle OAM the hypotenuse OM^2 =OA^2+AM^2
and OM =1 so 1 =(cos x)^2+(sinx)^2
Make my drawing

Answer 3

this come from
x^2+y^2=1 in the unit circle as
cos=x (x-axis represent cos)
sin=y (y-axis represent sin )