Question

Where does the Pythagorean Identity sin2 Θ + cos2 Θ = 1 come from? How 
does it relate to right triangles?

Answer 1

The Pythagorean Identity, sin^2(Θ) + cos^2(Θ) = 1, comes from the Pythagorean Theorem and relates the sine and cosine functions.

Step-by-step explanation:

The Pythagorean Identity, sin^2(Θ) + cos^2(Θ) = 1, is a trigonometric identity that relates the sine and cosine functions. It comes from the Pythagorean Theorem, which describes the relationship between the sides of a right triangle. In a right triangle, if we let one angle be Θ, the opposite side is sin(Θ) and the adjacent side is cos(Θ). By using the Pythagorean Theorem, we can derive the Pythagorean Identity.

Answer 2

I think you meant (sin theta)^2 and (cos theta)^2.

There is an identity stating that (sin theta)^2 + (cos theta)^2 = 1.

Please, don't write "sin2 theta;" it looks too much like sin 2(theta), which is completely different from (sin theta)^2.