Question

Dante and Jamile graphed $y=3\cos \left(\frac{2\theta }{3}\right)$. Who is correct? Explain your reasoning.

Short answer

The graph drawn of$y=3\cos \left(\frac{2\theta }{3}\right)$ by Jamile is correct.

Step-by-step solution

Step 1. Write down the given information.

The graph of $y=3\cos \left(\frac{2\theta }{3}\right)$ drawn by Dante and Jamile are shown below.

Step 2. Explanation.

From the given graphs of Dante and Jamile it can be seen that the amplitude of graph drawn by Dante is less than 1 unit whereas the amplitude of graph drawn by Jamile is 3 unit which matches with the amplitude of the given function $y=3\cos \left(\frac{2\theta }{3}\right)$. Hence, the graph drawn of $y=3\cos \left(\frac{2\theta }{3}\right)$ by Jamile is correct.

Step 3. Conclusion.

The graph drawn of $y=3\cos \left(\frac{2\theta }{3}\right)$ by Jamile is correct.