Question

O valor de tg (arcsen 4/5 ) é:

a) 3/5
b) 3/4
c) 4/3
d) 1
e) 0

Favor explicar passo a passo.

Answer 1

Sabe-se que:

$tg(arcsin(x))=\frac{x}{\sqrt{1-x^2}}$

Então,

$\frac{\frac{4}{5}}{\sqrt{1-\frac{4}{5}^2}}$

$\frac{4}{5\sqrt{1-\frac{16}{25}}}$

$\frac{4}{5\sqrt{\frac{9}{25}}}$

$\frac{4}{5\frac{3}{5}}$

$tg(arcsin(\frac{4}{5}))=\frac{4}{3}$

Alternativa C.