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Define tanh(t) in terms of exponentials

Whenever you have a define by exponentials question start with: sinh(t)=0.5(e t -e -t ) and cosh(t)=0.5(e t +e -t ) We know tanh(t)=sinh(t)/cosh(t) tanh(t)=0.5(e t -e -t )/0.5(e t +e -t ) =(e t -e -t )/(e t ...
NS
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How do I solve a simultaneous equation with more unknowns than equations?

If a set of equations has more unknowns than equations, you cannot get a value for each unknown. However, you can find the relationships between the variables.Start by rearranging one variable in terms of th...
HM
5593 Views

Given that abc = -37 + 36i; b = -2 + 3i; c = 1 + 2i, what is a?

Substituting the given values for b and c into the equation for abc , a (-2 + 3i)(1 + 2i) = -37 + 36i Multiplying out the terms in brackets, a (-2 - 4i + 3i - 6) = -37 + 36i Collecting like terms and multipl...
AS
4667 Views

Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).

De Moivre's Theorem states that if z = cos(q)+isin(q), then z n = (cos(q)+isin(q)) n = cos(nq)+isin(nq) But then z -n = cos(-nq)+isin(-nq). Now, cos(-p)=cos(p), as cosine is a symmetric (even) function, and ...
DA
18148 Views

Prove that matrix multiplication is not commutative.

At GCSE level, proof questions are relatively rare and largely will all require a similar sort of approach. The difference with A Level is that the syllabus contains more than one method of proof. You will b...
SF
23362 Views