State the amplitude and period of the function. Graph the function.

Select the correct response:

Question

State the amplitude and period of the function. Graph the function. $$ y=2 \sin 2 	heta $$ Select the correct response:

UpStudy AI · Accepted Answer

To analyze the function $$ y = 2 \sin 2\theta $$, we can identify the amplitude and period as follows:

1. **Amplitude**: The amplitude of a sine function $$ y = A \sin(B\theta) $$ is given by the absolute value of $$ A $$. In this case, $$ A = 2 $$, so the amplitude is:
   $$
   \text{Amplitude} = |2| = 2
   $$

2. **Period**: The period of a sine function is calculated using the formula:
   $$
   \text{Period} = \frac{2\pi}{B}
   $$
   where $$ B $$ is the coefficient of $$ \theta $$. Here, $$ B = 2 $$, so the period is:
   $$
   \text{Period} = \frac{2\pi}{2} = \pi
   $$

Now, let's graph the function $$ y = 2 \sin 2\theta $$.

I'll proceed to create the graph.
It seems that I cannot directly generate the graph at this moment. However, I can guide you on how to graph the function $$ y = 2 \sin 2\theta $$.

### Steps to Graph $$ y = 2 \sin 2\theta $$:

1. **Set up the axes**: Draw a horizontal axis (x-axis) for $$ \theta $$ and a vertical axis (y-axis) for $$ y $$.

2. **Mark the amplitude**: Since the amplitude is 2, mark points at $$ y = 2 $$ and $$ y = -2 $$ on the y-axis.

3. **Determine the period**: The period is $$ \pi $$. This means that the function will complete one full cycle from $$ \theta = 0 $$ to $$ \theta = \pi $$.

4. **Plot key points**:
   - At $$ \theta = 0 $$, $$ y = 2 \sin(0) = 0 $$.
   - At $$ \theta = \frac{\pi}{4} $$, $$ y = 2 \sin\left(2 \cdot \frac{\pi}{4}\right) = 2 \sin\left(\frac{\pi}{2}\right) = 2 $$.
   - At $$ \theta = \frac{\pi}{2} $$, $$ y = 2 \sin(\pi) = 0 $$.
   - At $$ \theta = \frac{3\pi}{4} $$, $$ y = 2 \sin\left(2 \cdot \frac{3\pi}{4}\right) = 2 \sin\left(\frac{3\pi}{2}\right) = -2 $$.
   - At $$ \theta = \pi $$, $$ y = 2 \sin(2\pi) = 0 $$.

5. **Draw the curve**: Connect these points smoothly, creating a wave that oscillates between 2 and -2, completing one cycle from $$ 0 $$ to $$ \pi $$.

### Summary:
- **Amplitude**: 2
- **Period**: $$ \pi $$

You can use graphing software or a graphing calculator to visualize this function accurately.
The amplitude is 2 and the period is $$ \pi $$. The graph of $$ y = 2 \sin 2\theta $$ oscillates between 2 and -2, completing one full cycle every $$ \pi $$ units.

State the amplitude and period of the function. Graph the function.

Select the correct response:

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State the amplitude and period of the function. Graph the function. Select the correct response:

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Beyond the Answer

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Latest Trigonometry Questions

State the amplitude and period of the function. Graph the function.

Select the correct response: