Question

Resolva 4cos²x=3 Considerando U = [0,2π[

Answer 1

Resposta:

S = { π/6, 11π/6, 5π/6, 7π/6 }

Explicação passo-a-passo:

.

4.cos^2 x = 3

Cos^2 x = 3/4

Cos x = +- √(3/4)

Cos x = +- √3 / 2

ENTÃO:

x = π/6 ..ou..x = 11π/6 ...ou .

x = 5π/6 ...ou...x = 7π/6

.

(Espero ter colaborado)

Answer 2

Explicação passo-a-passo:

$\sf 4\cdot cos^2~x=3$

$\sf cos^2~x=\dfrac{3}{4}$

$\sf cos~x=\pm\sqrt{\dfrac{3}{4}}$

$\sf cos~x=\pm\dfrac{\sqrt{3}}{2}$

• Para $\sf cos~x=\dfrac{\sqrt{3}}{2}$, temos:

$\sf x=30^{\circ}~\Rightarrow~x=\dfrac{\pi}{6}~rad$

$\sf x=330^{\circ}~\Rightarrow~x=\dfrac{11\pi}{6}~rad$

• Para $\sf cos~x=-\dfrac{\sqrt{3}}{2}$, temos:

$\sf x=150^{\circ}~\Rightarrow~x=\dfrac{5\pi}{6}~rad$

$\sf x=210^{\circ}~\Rightarrow~x=\dfrac{7\pi}{6}~rad$

Logo, $\sf S=\left\{\dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}\right\}$