Będziemy korzystać z tabelki wartości funkcji trygonometrycznych niektórych kątów.

	$30^{\circ }$	$45^{\circ }$	$60^{\circ }$
$\sin \alpha$	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$
$\cos \alpha$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$
$\mathrm{tg}\alpha$	$\frac{\sqrt{3}}{3}$	$1$	$\sqrt{3}$

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a)

$5\sin 30^{\circ }+4\cos 60^{\circ }+\mathrm{tg}45^{\circ }=5\cdot \frac{1}{2}+4\cdot \frac{1}{2}+1=\frac{5}{2}+2+1=2\frac{1}{2}+3=5\frac{1}{2}$

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b)

$3\sin 60^{\circ }-5\mathrm{tg}45^{\circ }+3\mathrm{tg}30^{\circ }=3\cdot \frac{\sqrt{3}}{2}-5\cdot 1+3\cdot \frac{\sqrt{3}}{3}=\frac{3\sqrt{3}}{2}-5+\sqrt{3}=\frac{5\sqrt{3}}{2}-5=\frac{5\sqrt{3}-10}{2}$

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c)

${\sin }^{2}30^{\circ }+{\cos }^{2}60^{\circ }+\mathrm{tg}45^{\circ }={\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^2+1=\frac{1}{4}+\frac{1}{4}+1=1\frac{1}{2}$

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d)

$\frac{3\sin 60^{\circ }}{{\sin }^{2}45^{\circ }+{\cos }^{2}45^{\circ }}=\frac{3\cdot \frac{\sqrt{3}}{2}}{{\left(\frac{\sqrt{2}}{2}\right)}^2+{\left(\frac{\sqrt{2}}{2}\right)}^2}=\frac{3\sqrt{3}}{2}:\left(\frac{1}{2}+\frac{1}{2}\right)=\frac{3\sqrt{3}}{2}$

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e)

$\frac{{\mathrm{tg}}^{2}30^{\circ }+{\cos }^{2}30^{\circ }}{3-2\mathrm{tg}45^{\circ }}=\frac{{\left(\frac{\sqrt{3}}{3}\right)}^2+{\left(\frac{\sqrt{3}}{2}\right)}^2}{3-2\cdot 1}=\left(\frac{1}{3}+\frac{3}{4}\right):1=\frac{4}{12}+\frac{9}{12}=\frac{13}{12}$

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f)

$\frac{2-{\mathrm{tg}}^{2}60^{\circ }}{\sin 30^{\circ }\cos 60^{\circ }}=\frac{2-{\left(\sqrt{3}\right)}^2}{\frac{1}{2}\cdot \frac{1}{2}}=\frac{2-3}{\frac{1}{4}}=\left(-1\right)\cdot 4=-4$

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g)

$\frac{12\cos 30^{\circ }-6\mathrm{tg}30^{\circ }}{4\sin 60^{\circ }}=\frac{12\cdot \frac{\sqrt{3}}{2}-6\cdot \frac{\sqrt{3}}{3}}{4\cdot \frac{\sqrt{3}}{2}}=\frac{6\sqrt{3}-2\sqrt{3}}{2\sqrt{3}}=\frac{4\sqrt{3}}{2\sqrt{3}}=2$

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h)

$2\sin 30^{\circ }+3\cos 60^{\circ }-4\mathrm{tg}45^{\circ }=2\cdot \frac{1}{2}+3\cdot \frac{1}{2}-4\cdot 1=1+\frac{3}{2}-4=-\frac{3}{2}$