Equivalence of Definitions for Sine and Cosine
From ProofWiki
Theorem
The definitions for sine and cosine are equivalent.
That is:
- $\displaystyle \sin x = \sum_{n=0}^\infty \left({-1}\right)^n \frac {x^{2n+1}}{\left({2n+1}\right)!} \iff \sin x = \frac {\text{Opposite}} {\text{Hypotenuse}}$
- $\displaystyle \cos x = \sum_{n=0}^\infty \left({-1}\right)^n \frac {x^{2n}}{\left({2n}\right)!} \iff \cos x = \frac {\text{Adjacent}} {\text{Hypotenuse}}$
Proof
You can help Proof Wiki by expanding it.
To discuss it in more detail, feel free to use the talk page.
When this page/section has been completed, {{Stub}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
