Question

Sabendo que o seno de x = 1/3, calcule:
a) cos x
b) tg x

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{sen^2\:x + cos^2\:x = 1}$

$\mathsf{cos^2\:x = 1 - sen^2\:x}$

$\mathsf{cos^2\:x = 1 - \large(\dfrac{1}{3}\large)^2}$

$\mathsf{cos^2\:x = 1 - \dfrac{1}{9}}$

$\mathsf{cos^2\:x = \dfrac{9 - 1}{9}}$

$\mathsf{cos^2\:x = \dfrac{8}{9}}$

$\boxed{\boxed{\mathsf{cos\:x = \pm\dfrac{2\sqrt{2}}{3}}}}$

$\mathsf{tg\:x = \dfrac{sen\:x}{cos\:x}}$

$\mathsf{tg\:x = \dfrac{1}{3} \times \dfrac{3}{2\sqrt{2}}}$

$\boxed{\boxed{\mathsf{tg\:x = \pm \dfrac{\sqrt{2}}{4}}}}$

Answer 2

Resposta:

sen(x)=1/3

sen²(x)+cos²(x)=1

cos²=1-sen²(x)

a)

cos²(x)=1-(1/3)²

cos²(x)=1-1/9

cos²(x)=8/9

cos(x)=±√8/3 =±2√2/3

bh)

tg(x)=sen(x)/cos(x) =(1/3)/[±2√2/3] =1/[±2√2]

=±√2/4