1,183 Pages ## Proof

### Prerequisites

• The antiderivative of 0 is a constant
• Series definition of sine and cosine (in particular and )
• Differential of is , differential of is • Linearity of the derivative, the Chain rule

### Proof  (linearity of the derivative) (chain rule) (evaluating the differentials) As the derivative of the expression is zero, this implies for some constant k. Evaluating at , which means , implying ## Geometric "proof"

It is possible to use geometry to prove the statement, however it only holds for ### Prerequisites

• Pythagorean Theorem: , in any right triangle. - [ Proof ]
• The definition of the trigonometric functions as ratios of the sides of a right triangle:
• sine: • cosine: ### Proof

Given an arbitrary right triangle, the following are true:  Here,  And therefore, Via the Pythagorean Theorem, the legs (here: opposite and adjacent) are "a," and "b" where hypotenuse is "c".   So, Community content is available under CC-BY-SA unless otherwise noted.