Gra edukacyjna

Polecenie 1

Zagraj w jędnorękiego bandytę. W grze poćwiczysz znajomość wartości funkcji trygonometrycznych połowy charakterystycznych kątów.

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Uzupełnij luki odpowiednimi liczbami. a)

\sin 15 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

\sin 67, 5 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

\sin 75 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

tg 15 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

tg 22, 5 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

tg 67, 5 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

tg 75 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

\cos 22, 5 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

\cos 15 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

\cos 75 ° =

2 - \sqrt{3}

, 2.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 3.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 4.

\sqrt{2} + 1

, 5.

\frac{\sqrt{2 + \sqrt{2}}}{2}

, 6.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 7.

2 + \sqrt{3}

, 8.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 9.

\frac{\sqrt{6} - \sqrt{2}}{4}

, 10.

\sqrt{2} - 1

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Polecenie 2

Oblicz wartość wyrażenia: $\frac{1 - {tg}^{2} 15 °}{1 + {tg}^{2} 15 °}$ .

$\frac{1 - {tg}^{2} 15 °}{1 + {tg}^{2} 15 °} =$

$= \frac{1 - \frac{\sin^{2} 15 °}{\cos^{2} 15 °}}{1 + \frac{\sin^{2} 15 °}{\cos^{2} 15 °}} = \frac{\cos^{2} 15 ° - \sin^{2} 15 °}{\cos^{2} 15 ° + \sin^{2} 15 °} =$

$= \frac{\cos^{2} 15 ° - \sin^{2} 15 °}{1} = \cos 30 ° = \frac{\sqrt{3}}{2}$

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