## One Cycle of a Trigonometric Function

Integral of a Complex Exponential Consider the integral $\int_0^{2 \pi} d\theta e^{i \theta}$. Upper Limit of $2 \pi$ Radians The upper limit is the number, $2 \pi$. For a circle with…

## Differentiating the Sine Function

From this post, one type of derivative is $\lim_{\Delta x\rightarrow0^+}\frac{f(a+\Delta x)-f(a)}{\Delta x}\equiv\frac{df(x)}{dx}\big|_{a^+}$ To be consistent with my previous interpretation of $0^+$ in this post, $\Delta x \rightarrow 0^+$ means constraining $\Delta x$ to positive numbers. Next, define…

What is $\lim_{x\rightarrow0} \frac{\sin x}{x}$ ? Recall the definition of a limit, repeated here for reference [2]. A function $f(x)$ approaches a limit $A$ as $x$ approaches $a$ if, and only if, for each…
This post includes proofs of two angle addition identities. $\sin(x+y) = \sin x \cos y + \sin y \cos x$ $\cos(x+y) = \cos x \cos y – \sin x \sin y$…