Question

What is the equation of the graph below?

Answer 1

Option B is the correct answer.

Step-by-step explanation:

From the graph we can see that

           $y\left ( \frac{2\pi}{3}\right )=0$

Substituting in all the options given,

Option A

      $y=sin\left ( \frac{x}{3}\right )\\\\y\left ( \frac{2\pi}{3}\right )=sin\left ( \frac{\frac{2\pi}{3}}{3}\right )\\\\y\left ( \frac{2\pi}{3}\right )=sin\left ( \frac{2\pi}{9}\right )=0.643\\\\y\left ( \frac{2\pi}{3}\right )=0.643\neq 0$

      Option A is not correct.

Option B

      $y=sin3x\\\\y\left ( \frac{2\pi}{3}\right )=sin\left (3\times \frac{2\pi}{3} \right )\\\\y\left ( \frac{2\pi}{3}\right )=sin2\pi=0\\\\y\left ( \frac{2\pi}{3}\right )=0=0$

      Option B is correct.  

Option C

      $y=sin0.3x\\\\y\left ( \frac{2\pi}{3}\right )=sin\left (0.3\times \frac{2\pi}{3} \right )\\\\y\left ( \frac{2\pi}{3}\right )=sin0.2\pi=0\\\\y\left ( \frac{2\pi}{3}\right )=0.588\neq 0$

      Option C is not correct.

Option D

      $y=sin\left ( \frac{2x}{3}\right )\\\\y\left ( \frac{2\pi}{3}\right )=sin\left ( \frac{\frac{2\times 2\pi}{3}}{3}\right )\\\\y\left ( \frac{2\pi}{3}\right )=sin\left ( \frac{4\pi}{9}\right )=0.985\\\\y\left ( \frac{2\pi}{3}\right )=0.985\neq 0$

      Option D is not correct.

Option B is the correct answer.

Answer 2

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.