What is the amplitude, period and frequency for the function $y = - 1 + \frac{1}{3} cot 2 x$ $y=-1+\frac{1}{3} \cot 2x$ ?

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\int_{0}^{1} \int_{0}^{\sqrt{1 - x^{2}}} \int_{\sqrt{x^{2} + y^{2}}}^{\sqrt{2 - x^{2} - y^{2}}} x y d z d y d x

$int_0^1int_0^sqrt(1-x^2)int_sqrt(x^2+y^2)^sqrt(2-x^2-y^2)xydzdydx$ to cylindrical or spherical coordinates?"

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Answer 1 · 2015-02-26T21:02:40

The cotangent has no Amplitude, because it assumes every value in $(- \infty, + \infty)$ $(-oo,+oo)$ .

Let $f (x)$ $f(x)$ be a periodic function:

$y = f (k x)$ $y=f(kx)$

has the period:

$T_{f (k x)} = \frac{T_{f (x)}}{k}$ $T_f(kx)=T_f(x)/k$ .

So, since the cotangent has period $π$ $pi$ ,

$T_{cot (2 x)} = \frac{π}{2}$ $T_cot(2x)=pi/2$

The frequency is $f = \frac{1}{T} = \frac{2}{π}$ $f=1/T=2/pi$ .

What is the amplitude, period and frequency for the function y=-1+\frac{1}{3} \cot 2xy=−1+13cot2xy=-1+\frac{1}{3} \cot 2x?