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Further Mathematics
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Explain the process of using de Moivre's Theorem to find a trigonometric identity. For example, express tan(3x) in terms of sin(x) and cos(x).

  1. Identify de Moivre's Theorem: (cos(x) + isin(x))n = cos(nx) + isin(nx) 2) Deduce the correct value of n for the given problem. In this e...
Answered by Ollie L. Further Mathematics tutor
3228 Views

For a homogeneous second order differential equation, why does a complex conjugate pair solution (m+in and m-in) to the auxiliary equation result in the complementary function y(x)=e^(mx)(Acos(nx)+Bisin(nx)), where i represents √(-1).

For a second order differential equation, our auxiliary equation, am2+bm+c=0, has two roots. Let's denote these roots as A and B. Note that A and B can be the same if there is a repeated root, ...

Answered by Joshua B. Further Mathematics tutor
2223 Views

State the conditions by which a Poisson distribution model may be suitable for a given random variable X.

The events recorded by X occur randomly, independently, singly in space and time and at a constant average rate (an average (mean) rate proportional to the length of the interval).

Answered by Kai C. Further Mathematics tutor
1728 Views

How do I integrate arctan(x) using integration by parts?

This is an example where we use integration by parts, but it is not immediately obvious where to start.Recall the integration by parts formula ∫u(dv/dx) dx = uv - ∫(du/dx)v dx
KEY STEP:

Answered by Oliver C. Further Mathematics tutor
9569 Views

Integrate xsin(x).

The technique we need to use to solve this integral is called integration by parts. The parts formula is: the integral of (uv' dx) = uv - the integral of (u'v dx) (where u and v are functions of x). We ne...

Answered by Jakub W. Further Mathematics tutor
2060 Views

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