2

mrkotukofficial @mrkotukofficial

August 2022 1 3 Report

Дан tgα= - 1/3

3П/2<α<2П

Найти:
cosα-?
sinα-?
ctgα-?

α - это альфа.

подробненько.

Answers & Comments

Miroslava227

Ответ:

$\tan( \alpha ) = - \frac{1}{3} \\$

IV четверть => синус отрицательный, косинус положительный, котангенс отрицательный.

$\cot( \alpha ) = \frac{1}{ \tan( \alpha ) } = \frac{1}{ - \frac{1}{3} } = - 3$

Далее используем формулу:

$1 + { \tan( \alpha ) }^{2} = \frac{1}{ { \cos( \alpha ) }^{2} }$

$\frac{1}{ { \cos( \alpha ) }^{2} } = 1 + \frac{1}{9} = \frac{10}{9} \\ { \cos( \alpha ) }^{2} = \frac{9}{10} \\ \cos( \alpha ) = \sqrt{ \frac{9}{10} } = \frac{3}{ \sqrt{10} }$

${ \sin( \alpha ) }^{2} = 1 - { \cos( \alpha ) }^{2}$

$\sin( \alpha ) = - \sqrt{1 - { \cos( \alpha ) }^{2} } = - \sqrt{1 - \frac{9}{10} } = - \sqrt{ \frac{1}{10} } = - \frac{1}{ \sqrt{10} }$

Ответ:

$\cos( \alpha ) = \frac{3}{ \sqrt{10} } \\ \sin( \alpha ) = - \frac{1}{ \sqrt{10} } \\ \cot( \alpha ) = - 3$

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