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iss #1386 lang packs markdown tables calc_diff_standard and greek_alp…
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hayden-MB committed Feb 6, 2025
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272 changes: 218 additions & 54 deletions lang/en/qtype_stack.php
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';

$string['greek_alphabet_name'] = 'The Greek Alphabet';
$string['greek_alphabet_fact'] = '||||
|--- |--- |--- |
|Upper case, \(\quad\)|lower case, \(\quad\)|name|
|\(A\)|\(\alpha\)|alpha|
|\(B\)|\(\beta\)|beta|
|\(\Gamma\)|\(\gamma\)|gamma|
|\(\Delta\)|\(\delta\)|delta|
|\(E\)|\(\epsilon\)|epsilon|
|\(Z\)|\(\zeta\)|zeta|
|\(H\)|\(\eta\)|eta|
|\(\Theta\)|\(\theta\)|theta|
|\(K\)|\(\kappa\)|kappa|
|\(M\)|\(\mu\)|mu|
|\(N\)|\( u\)|nu|
|\(\Xi\)|\(\xi\)|xi|
|\(O\)|\(o\)|omicron|
|\(\Pi\)|\(\pi\)|pi|
|\(I\)|\(\iota\)|iota|
|\(P\)|\(\rho\)|rho|
|\(\Sigma\)|\(\sigma\)|sigma|
|\(\Lambda\)|\(\lambda\)|lambda|
|\(T\)|\(\tau\)|tau|
|\(\Upsilon\)|\(\upsilon\)|upsilon|
|\(\Phi\)|\(\phi\)|phi|
|\(X\)|\(\chi\)|chi|
|\(\Psi\)|\(\psi\)|psi|
|\(\Omega\)|\(\omega\)|omega|';
$string['greek_alphabet_fact'] = '<table>
<thead>
<tr>
<th></th>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>Upper case, (\quad)</td>
<td>lower case, (\quad)</td>
<td>name</td>
</tr>
<tr>
<td>(A)</td>
<td>(\alpha)</td>
<td>alpha</td>
</tr>
<tr>
<td>(B)</td>
<td>(\beta)</td>
<td>beta</td>
</tr>
<tr>
<td>(\Gamma)</td>
<td>(\gamma)</td>
<td>gamma</td>
</tr>
<tr>
<td>(\Delta)</td>
<td>(\delta)</td>
<td>delta</td>
</tr>
<tr>
<td>(E)</td>
<td>(\epsilon)</td>
<td>epsilon</td>
</tr>
<tr>
<td>(Z)</td>
<td>(\zeta)</td>
<td>zeta</td>
</tr>
<tr>
<td>(H)</td>
<td>(\eta)</td>
<td>eta</td>
</tr>
<tr>
<td>(\Theta)</td>
<td>(\theta)</td>
<td>theta</td>
</tr>
<tr>
<td>(K)</td>
<td>(\kappa)</td>
<td>kappa</td>
</tr>
<tr>
<td>(M)</td>
<td>(\mu)</td>
<td>mu</td>
</tr>
<tr>
<td>(N)</td>
<td>( u)</td>
<td>nu</td>
</tr>
<tr>
<td>(\Xi)</td>
<td>(\xi)</td>
<td>xi</td>
</tr>
<tr>
<td>(O)</td>
<td>(o)</td>
<td>omicron</td>
</tr>
<tr>
<td>(\Pi)</td>
<td>(\pi)</td>
<td>pi</td>
</tr>
<tr>
<td>(I)</td>
<td>(\iota)</td>
<td>iota</td>
</tr>
<tr>
<td>(P)</td>
<td>(\rho)</td>
<td>rho</td>
</tr>
<tr>
<td>(\Sigma)</td>
<td>(\sigma)</td>
<td>sigma</td>
</tr>
<tr>
<td>(\Lambda)</td>
<td>(\lambda)</td>
<td>lambda</td>
</tr>
<tr>
<td>(T)</td>
<td>(\tau)</td>
<td>tau</td>
</tr>
<tr>
<td>(\Upsilon)</td>
<td>(\upsilon)</td>
<td>upsilon</td>
</tr>
<tr>
<td>(\Phi)</td>
<td>(\phi)</td>
<td>phi</td>
</tr>
<tr>
<td>(X)</td>
<td>(\chi)</td>
<td>chi</td>
</tr>
<tr>
<td>(\Psi)</td>
<td>(\psi)</td>
<td>psi</td>
</tr>
<tr>
<td>(\Omega)</td>
<td>(\omega)</td>
<td>omega</td>
</tr>
</tbody>
</table>
';

$string['alg_inequalities_name'] = 'Inequalities';
$string['alg_inequalities_fact'] = '\[a>b \hbox{ means } a \hbox{ is greater than } b.\]
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\[\tanh^{-1}(x) = \frac{1}{2}\ln\left({1+x\over 1-x}\right) \quad \text{ for } -1< x < 1\]';

$string['calc_diff_standard_derivatives_name'] = 'Standard Derivatives';
$string['calc_diff_standard_derivatives_fact'] = 'The following table displays the derivatives of some standard functions. It is useful to learn these standard derivatives as they are used frequently in calculus.
|\(f(x)\)|\(f\'(x)\)|
|--- |--- |
|\(k\), constant|\(0\)|
|\(x^n\), any constant \(n\)|\(nx^{n-1}\)|
|\(e^x\)|\(e^x\)|
|\(\ln(x)=\log_{\rm e}(x)\)|\(\frac{1}{x}\)|
|\(\sin(x)\)|\(\cos(x)\)|
|\(\cos(x)\)|\(-\sin(x)\)|
|\(\tan(x) = \frac{\sin(x)}{\cos(x)}\)|\(\sec^2(x)\)|
|\(cosec(x)=\frac{1}{\sin(x)}\)|\(-cosec(x)\cot(x)\)|
|\(\sec(x)=\frac{1}{\cos(x)}\)|\(\sec(x)\tan(x)\)|
|\(\cot(x)=\frac{\cos(x)}{\sin(x)}\)|\(-cosec^2(x)\)|
|\(\cosh(x)\)|\(\sinh(x)\)|
|\(\sinh(x)\)|\(\cosh(x)\)|
|\(\tanh(x)\)|\(sech^2(x)\)|
|\(sech(x)\)|\(-sech(x)\tanh(x)\)|
|\(cosech(x)\)|\(-cosech(x)\coth(x)\)|
|\(coth(x)\)|\(-cosech^2(x)\)|
\[ \frac{d}{dx}\left(\sin^{-1}(x)\right) = \frac{1}{\sqrt{1-x^2}}\]
\[ \frac{d}{dx}\left(\cos^{-1}(x)\right) = \frac{-1}{\sqrt{1-x^2}}\]
\[ \frac{d}{dx}\left(\tan^{-1}(x)\right) = \frac{1}{1+x^2}\]
\[ \frac{d}{dx}\left(\cosh^{-1}(x)\right) = \frac{1}{\sqrt{x^2-1}}\]
\[ \frac{d}{dx}\left(\sinh^{-1}(x)\right) = \frac{1}{\sqrt{x^2+1}}\]
\[ \frac{d}{dx}\left(\tanh^{-1}(x)\right) = \frac{1}{1-x^2}\]
$string['calc_diff_standard_derivatives_fact'] = '<p>The following table displays the derivatives of some standard functions. It is useful to learn these standard derivatives as they are used frequently in calculus.</p>
<table>
<thead>
<tr>
<th>(f(x))</th>
<th>(f\&#39;(x))</th>
</tr>
</thead>
<tbody>
<tr>
<td>(k), constant</td>
<td>(0)</td>
</tr>
<tr>
<td>(x^n), any constant (n)</td>
<td>(nx^{n-1})</td>
</tr>
<tr>
<td>(e^x)</td>
<td>(e^x)</td>
</tr>
<tr>
<td>(\ln(x)=\log_{\rm e}(x))</td>
<td>(\frac{1}{x})</td>
</tr>
<tr>
<td>(\sin(x))</td>
<td>(\cos(x))</td>
</tr>
<tr>
<td>(\cos(x))</td>
<td>(-\sin(x))</td>
</tr>
<tr>
<td>(\tan(x) = \frac{\sin(x)}{\cos(x)})</td>
<td>(\sec^2(x))</td>
</tr>
<tr>
<td>(cosec(x)=\frac{1}{\sin(x)})</td>
<td>(-cosec(x)\cot(x))</td>
</tr>
<tr>
<td>(\sec(x)=\frac{1}{\cos(x)})</td>
<td>(\sec(x)\tan(x))</td>
</tr>
<tr>
<td>(\cot(x)=\frac{\cos(x)}{\sin(x)})</td>
<td>(-cosec^2(x))</td>
</tr>
<tr>
<td>(\cosh(x))</td>
<td>(\sinh(x))</td>
</tr>
<tr>
<td>(\sinh(x))</td>
<td>(\cosh(x))</td>
</tr>
<tr>
<td>(\tanh(x))</td>
<td>(sech^2(x))</td>
</tr>
<tr>
<td>(sech(x))</td>
<td>(-sech(x)\tanh(x))</td>
</tr>
<tr>
<td>(cosech(x))</td>
<td>(-cosech(x)\coth(x))</td>
</tr>
<tr>
<td>(coth(x))</td>
<td>(-cosech^2(x))</td>
</tr>
</tbody>
</table>
<p> [ \frac{d}{dx}\left(\sin^{-1}(x)\right) = \frac{1}{\sqrt{1-x^2}}]
[ \frac{d}{dx}\left(\cos^{-1}(x)\right) = \frac{-1}{\sqrt{1-x^2}}]
[ \frac{d}{dx}\left(\tan^{-1}(x)\right) = \frac{1}{1+x^2}]
[ \frac{d}{dx}\left(\cosh^{-1}(x)\right) = \frac{1}{\sqrt{x^2-1}}]
[ \frac{d}{dx}\left(\sinh^{-1}(x)\right) = \frac{1}{\sqrt{x^2+1}}]
[ \frac{d}{dx}\left(\tanh^{-1}(x)\right) = \frac{1}{1-x^2}]</p>
';

$string['calc_diff_linearity_rule_name'] = 'The Linearity Rule for Differentiation';
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