Найдите sina, cosa и ctga, если tg=0.75 и a-острый угол. Created by rahima2000kg. geometriya-ru

Найдите sina, cosa и ctga, если tg=0.75 и a-острый угол...

rahima2000kg @rahima2000kg

August 2022 1 0 Report

Найдите sina, cosa и ctga, если tg=0.75 и a-острый угол

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kDmitry $tg \alpha =0,75= \frac{3}{4}$

$tg \alpha = \frac{sin \alpha }{cos \alpha }$

$1+ tg^{2} \alpha = \frac{1}{ cos^{2} \alpha }$

$cos ^{2} \alpha = \frac{1}{ tg^{2} \alpha +1 }$

$cos \alpha =\sqrt{ \frac{1}{ \frac{9}{16} +1 } } = \sqrt{ \frac{1}{ \frac{9}{16} + \frac{16}{16} } }= \sqrt{ \frac{1}{ \frac{25}{16} } }= \sqrt{ \frac{16}{25} }= \frac{4}{5}$

$sin \alpha = \sqrt{1- cos^{2} \alpha } = \sqrt{1- \frac{16}{25} }= \sqrt{ \frac{25}{25}- \frac{16}{25} }= \sqrt{ \frac{9}{25} }= \frac{3}{5}$

$ctg \alpha = \frac{1}{tg \alpha } = \frac{4}{3}$

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