Q44. - Algebra 2

Question

Identify the equation of the graphed function.

$\begin{array}{c}\left(A\right)y=\frac{1}{2}\sin \left(4\theta \right)\\ \left(B\right)y=2\sin \left(\frac{1}{4}\theta \right)\\ \left(C\right)y=\frac{1}{4}\sin \left(2\theta \right)\\ \left(D\right)y=4\sin \left(\frac{1}{2}\theta \right)\end{array}$

Step-by-Step Solution

Answer

The equation of the graphed function is $y=\frac{1}{4}\sin \left(2\theta \right)$. So, option (C) is correct.

Step 1. Write down the given information.

The given graphed function is shown below.

Step 2. Evaluating amplitude and period of the given function.

By drawing a horizontal parallel line on two crests, it can be interpreted that, the amplitude of the given graphed function is $0.25$ which will be equivalent to $\frac{1}{4}$ in fraction form. And, the graph repeats itself after an interval of $\left(\pi \right)$. So, period of the graphed function is $\pi$.

 Now, from the given options (A), (B), (C) and (D), only option $\left(C\right)y=\frac{1}{4}\sin \left(2\theta \right)$ has amplitude of $\frac{1}{4}$ and period $\frac{2\pi }{2}=\pi$.

The equation of the graphed function is $y=\frac{1}{4}\sin \left(2\theta \right)$. So, option (C) is correct.

Step 3. Conclusion.

The equation of the graphed function is $y=\frac{1}{4}\sin \left(2\theta \right)$. So, option (C) is correct.