[tex]zad.2\\
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sin\alpha =\dfrac{2}{5} ~~\land ~~\alpha \in (90^{0} ,180^{0} )\\
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sin^{2} \alpha +cos^{2} \alpha =1~~\land~~sin\alpha =\dfrac{2}{5} \\
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cos^{2} \alpha +(\frac{2}{5} )^{2} =1\\
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cos^{2} \alpha=1-\dfrac{4}{25} \\
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cos^{2} \alpha=\dfrac{21}{25} ~~\land~~\alpha \in (90^{0} ,180^{0} )~~\Rightarrow ~~cos\alpha =-\dfrac{\sqrt{21} }{5} \\
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tg\alpha =\dfrac{sin\alpha }{cos\alpha } ~~\land~~cos\alpha =-\dfrac{\sqrt{21} }{5} ~~\land ~~sin\alpha =\dfrac{2}{5}\\
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[/tex]
[tex]tg\alpha =\dfrac{\dfrac{2}{5} }{-\dfrac{\sqrt{21} }{5} } =-\dfrac{2}{\sqrt{21} } \\
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tg\alpha =-\dfrac{2}{\sqrt{21} } \cdot \dfrac{\sqrt{21} }{\sqrt{21} }\\
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tg\alpha =-\dfrac{2\sqrt{21} }{21} [/tex]
[tex]Pamietaj:~~II~~cwiartka~~tylko~~sinus~~jest~~dodatni.[/tex]
[tex]zad.1\\
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a_{n} =a_{1} \cdot q^{n-1} ~~~~n-ty ~~wyraz~~ciagu~~geometrycznego\\
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a_{2} =a_{1} \cdot q~~\land ~~a_{2} =9 ~~\Rightarrow ~~a_{1} \cdot q=9\\
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a_{4} =a_{1} \cdot q^{3} ~~\land ~~a_{4} =1 ~~\Rightarrow ~~a_{1} \cdot q^{3} =1\\
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a_{1} \cdot q^{3} =1\\
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a_{1} \cdot q\cdot q^{2} =1~~\land ~~a_{1} \cdot q=9~~\Rightarrow ~~9\cdot q^{2} =1\\
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9\cdot q^{2} =1~~\mid \div 9\\
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q^{2}=\dfrac{1}{9}\\
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q=\dfrac{1}{3} ~~\lor~~q=-\dfrac{1}{3} \\
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[/tex]
[tex]a_{1} \cdot q=9~~\Rightarrow ~~a_{1} =\dfrac{9}{q} \\
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(~~q=\dfrac{1}{3} ~~\land ~~a_{1} =27~~)~~\lor ~~(~~q=-\dfrac{1}{3} ~~\land ~~a_{1} =-27~~)[/tex]
