Question

a) y=4sen(x)
arco
4sen(×)
y​

Answer 1

Olá, bom dia ◉‿◉.

$\boxed{ \begin{array}{r|c|c}arco&y = 4 \sin(x) &y \\ \\ 0&y = 4 \sin(0) &0 \\ \\ \frac{\pi}{2} &y = 4 \sin( \frac{\pi}{2} ) & 4\\ \\ \pi&y = 4 \sin(\pi) &0 \\ \\ \frac{3\pi}{2} &y = 4 \sin( \frac{3\pi}{2} ) & - 4 \\ \\ 2\pi&y = 4 \sin(2\pi) &0 \end{array}}$

Vamos identificar os valores dos senos desses arcos.

$\boxed{ \begin{cases} \sin(0) = 0 \\ \\ \sin( \frac{\pi}{2} ) = \sin(90 {}^{ \circ} ) = 1 \\ \\ \sin(\pi) = \sin(180 {}^{ \circ} ) = 0 \\ \\ \sin( \frac{3\pi}{2} ) = \sin(270 {}^{ \circ} ) = - 1 \\ \\ \sin(2\pi) = \sin(360 {}^{ \circ} ) = 0 \end{cases}}$

Agora vamos calcular.

I) Cálculos:

$a)y = 4 \sin(x) \\ y = 4 \sin(0) \\ y = 4.0 \\ \boxed{y = 0 } \\ \\ \\ \\ b) y = 4 \sin(x) \\ y = 4 \sin( \frac{\pi}{2} ) \\ y = 4.1 \\ \boxed{y = 4} \\ \\ \\ c)y = 4 \sin(x) \\ y = 4 \sin(\pi) \\ y = 4.0 \\ \boxed{ y = 0} \\ \\ \\ d) y = 4 \sin(x) \\ y = 4 \sin( \frac{3\pi}{2} ) \\ y = 4.( - 1) \\ \boxed{y = - 4} \\ \\ \\ e)y = 4 \sin(x) \\ y = 4 \sin(2\pi) \\ y = 4.0 \\ \boxed{ y = 0}$

Substituindo na tabela ↑.

Espero ter ajudado

Bons estudos ♥️