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and then jump to saying that since $\cos^2t + \sin^2t = 1$, $$\frac{x - x_0}a = \cos t\text{ and }\frac{y ...

Dec 21, 2014 · I was asked to find the Laplace transform of the function $\\displaystyle f(t)=te^{-t}\\sin(2t)$ using only the properties of Laplace transform, meaning, use clever tricks and the table shown at http...

$\eqalign{ & y = \sin (2t) \cr & x = \cos (t) \cr} $ therefore: $\eqalign{ & \sin (t) = {y \over {2\cos t}} \cr as: & \cos (t) = x \cr & {\rm{ sin(t) = }}{y ...

Mar 7, 2019 · Take a look at the following function: $$ x(t) = \\sin^3(2t) $$ In order to show the periodicity of the signal, we need to prove the following equality $$ x(t) = x(t+T) $$ We first use some trigonom...

${dy\over du} = (e^{2t\sin v})((2t)(\cos(2t)(2))+(\sin(2t))(2))(2)$ But then I learn that that last part "$(2)$" at the end of the equation is incorrect (note I don't need to simplify right now as I'm just learning how to use the chain rule).

Nov 8, 2013 · The area of the each of these is then $\frac 12 \sin t\cos t$ and together their area is $\sin t\cos t$ The lenght of the blue line is $\sin 2t$ Using that as the height at $1$ as the base gives the area of the large tringle as $\frac 12 \sin 2t$ We have now calculated the same area by two different methods and they must be equal.

This is an infinite-dimensional linear problem, because the space $\mathbb{R}^\mathbb{R}$ of real functions of a real variable has not finite dimension.

Nov 29, 2015 · Proof: $$2\cos(t)\cos(2t)-\sin(t)\sin(2t)=\frac{\cos(t)+3\cos(3t)}{2}\Longleftrightarrow$$ $$2\left(2\cos(t)\cos(2t)-\sin(t)\sin(2t)\right)=\cos(t)+3\cos(3t ...