Question

5. (CEP-BJ) Determine a soma das duas menores soluções positivas da equação sen (3x-pi/4)=0

Answer 1

$\sin(3x - \frac{\pi}{4} ) = 0 \\ 3x - \frac{\pi}{4} = 0 \: \: ou \: 3x - \frac{\pi}{4} = \pi$

$3x - \frac{\pi}{4} = 0 \\ 3x = \frac{\pi}{4} \\ 12x = \pi \\ x = \frac{\pi}{12}$

$3x - \frac{\pi}{4} = \pi \\ \frac{36x - 3\pi = 12\pi}{12} \\ 36x - 3\pi = 12\pi$

$36x = 3\pi + 12\pi \\ 36x = 15\pi \\ x = \frac{15\pi}{36} \\ x = \frac{5\pi}{12}$

Somando teremos.

$\frac{\pi}{12} + \frac{5\pi }{12} = \frac{6\pi}{12} = \frac{\pi}{2}$