Question

Considerando o triângulo retângulo abaixo

Answer 1

a)

$seno( \alpha ) = \frac{8}{10} = \frac{4}{5}$

b)

$cosseno( \alpha ) = \frac{6}{10} = \frac{3}{5}$

c)

$tangente( \alpha ) = \frac{8}{6} = \frac{4}{3}$

d)

$\frac{seno( \alpha )}{cosseno( \alpha )} = \frac{ \frac{4}{5} }{ \frac{3}{5} } = \frac{4}{5} \times \frac{5}{3} = \frac{20}{15} = \frac{4}{3} \\ \\ \frac{seno( \alpha )}{cosseno( \alpha )} =tangente( \alpha )$

e)

${seno}^{2} ( \alpha ) + {cosseno}^{2} ( \alpha ) = 1 \\ \\ ( \frac{4}{5} ) {}^{2} + ( \frac{3}{5} ) {}^{2} \\ \\ \frac{16}{25} + \frac{9}{25} = \frac{25}{25} = 1$

f)

$seno( \beta ) = \frac{6}{10} = \frac{3}{5}$

g)

$cosseno( \beta ) = \frac{8}{10} = \frac{4}{5}$

h)

$tangente( \beta ) = \frac{6}{8} = \frac{3}{4}$

i)

$\frac{seno( \beta )}{cosseno( \beta )} = tagente( \beta ) = \frac{3}{4}$

j)

${seno}^{2} ( \beta ) + {cosseno}^{2} ( \beta ) = 1$