If the trigonometric functions are defined in terms of geometry, then their derivatives can be found by first verifying that limx->∞ sin x / x = 1 and...; if they are defined by their Taylor series, then the derivatives can be found by differentiating the power series term by term. |
If the trigonometric functions are defined in terms of geometry, then their derivatives can be found by first verifying that limx->∞ sin x / x = 1 and then using the limit definition of the derivative and the addition theorems; if they are defined by their Taylor series, then the derivatives can be found by differentiating the power series term by term. |