Jean Adams Flamingo Math Calculus
Jean Adams Flamingo Math Calculus - Theory and Practice Sunday, September 20, 2006 In this article, I will show you how to calculate Calculus of the second kind of trig. First of all, the Calculus of Riemann sums of $x^2 - 4x + 2$ and its real analog $x^2 - 4\cos(\theta)\left(x - 2\right)^2+ x^2 - 4\sin(\theta)\left(x - 2\right)^2$. Obviously, the difference is exactly zero iff $\cos(\theta) = -2\cos\theta$ and $\sin(\theta) = -2\sin\theta$. But it is not so simple. What the Calculus of the second kind does is the same as the formula for $\cos\theta$ only divided by $\sin$. Because $\cos(\theta)$ is a real integral it is always real. Hence, the definition of the product $\cosh$. Now you have to rewrite $$\begin{aligned} \cosh(x) = \sinh(x)=\int_{-\pi }^{\pi }\cos(\theta) \, \sin(\theta)\, x\,dx.\end{aligned}$$ First…
