Question

Resolva as equações seguintes, considerando U = [0, 2π[.

A) cos x = 0
B) cos x = √2/2
C) cos x = 1
D) cos x = - 1/2
E) 3 * cos x + 6 = 0
F) 4 * cos² x = 3

Answer 1

Explicação passo a passo:

Item a:

$\cos{x}=0\\\\S=\{\frac{\pi}{2};\frac{3\pi}{2}\}$

Item b:

$\cos{x}=\frac{\sqrt{2}}{2}\\\\S=\{\frac{\pi}{4};\frac{7\pi}{4}\}$

Item c:

$\cos{x}=1\\\\S=\{0\}$

Item d:

$\cos{x}=-\frac{1}{2}\\\\S=\{\frac{2\pi}{3}; \frac{4\pi}{3}\}$

Item e:

$3\cdot \cos{x} + 6 = 0\\\\3\cdot \cos{x} = -6\\\\\cos{x} = -2\\\\S = \emptyset$

Item f:

$4\cdot \cos^2{x} = 3\\\\\cos^2{x}=\frac{3}{4}\\\\\cos{x} = \pm \frac{\sqrt{3}}{2}\\\\S=\{\frac{\pi}{6};\frac{5\pi}{6};\frac{7\pi}{6};\frac{11\pi}{6}\}$