Question

determine os valores de sen a, cos a, tg a, sen b, cos b e tg b.

Answer 1

$sen~\theta=\dfrac{cateto~oposto~ao~\^angulo~\theta}{hipotenusa}\\\\\\cos~\theta=\dfrac{cateto~adjacente~ao~\^angulo~\theta}{hipotenusa}\\\\\\tg~\theta=\dfrac{cateto~oposto~ao~\^angulo~\theta}{cateto~adjacente~ao~\^angulo~\theta}=\dfrac{sen~\theta}{cos~\theta}$

Quando temos ângulos complementares, que é o caso de α e β:

$sen~\alpha=cos~\beta\\sen~\beta=cos~\alpha\\tg~\alpha=(tg~\beta)^{-1}$
________________________

Calculando sen α:

$sen~\alpha=\dfrac{cateto~oposto~a~\alpha}{hipotenusa}\\\\\\\boxed{\boxed{sen~\alpha=\dfrac{7}{25}}}$

Calculando cos α:

$cos~\alpha=\dfrac{cateto~adjacente~a~\alpha}{hipotenusa}\\\\\\\boxed{\boxed{cos~\alpha=\dfrac{24}{25}}}$

Calculando tg α:

$tg~\alpha=\dfrac{cateto~oposto~a~\alpha}{cateto~adjacente~a~\alpha}\\\\\\\boxed{\boxed{tg~\alpha=\dfrac{7}{24}}}$

Calculando sen β:

$sen~\beta=cos~\alpha=\dfrac{24}{25}$

Calculando cos β:

$cos~\beta=sen~\alpha=\dfrac{7}{25}$

Calculando tg β:

$tg~\beta=\dfrac{cateto~oposto~a~\beta}{cateto~adjacente~a~\beta}=\dfrac{24}{7}$