Answer:
y = sin 3x.
Step-by-step explanation:
We see from the graph that y = sin 2π/3 = 0.
Let x = 2π/3 , then substituting in y = sin 3x we get
y = sin 3 * (2π/3) = sin 2π = 0.
Step-by-step explanation:
From the graph we can see that
[tex]y\left ( \frac{2\pi}{3}\right )=0[/tex]
Substituting in all the options given,
Option A
[tex]y=sin\left ( \frac{x}{3}\right )\\\\y\left ( \frac{2\pi}{3}\right )=sin\left ( \frac{\frac{2\pi}{3}}{3}\right )\\\\y\left ( \frac{2\pi}{3}\right )=sin\left ( \frac{2\pi}{9}\right )=0.643\\\\y\left ( \frac{2\pi}{3}\right )=0.643\neq 0[/tex]
Option A is not correct.
Option B
[tex]y=sin3x\\\\y\left ( \frac{2\pi}{3}\right )=sin\left (3\times \frac{2\pi}{3} \right )\\\\y\left ( \frac{2\pi}{3}\right )=sin2\pi=0\\\\y\left ( \frac{2\pi}{3}\right )=0=0[/tex]
Option B is correct.
Option C
[tex]y=sin0.3x\\\\y\left ( \frac{2\pi}{3}\right )=sin\left (0.3\times \frac{2\pi}{3} \right )\\\\y\left ( \frac{2\pi}{3}\right )=sin0.2\pi=0\\\\y\left ( \frac{2\pi}{3}\right )=0.588\neq 0[/tex]
Option C is not correct.
Option D
[tex]y=sin\left ( \frac{2x}{3}\right )\\\\y\left ( \frac{2\pi}{3}\right )=sin\left ( \frac{\frac{2\times 2\pi}{3}}{3}\right )\\\\y\left ( \frac{2\pi}{3}\right )=sin\left ( \frac{4\pi}{9}\right )=0.985\\\\y\left ( \frac{2\pi}{3}\right )=0.985\neq 0[/tex]
Option D is not correct.
Option B is the correct answer.