Question

Complete the table of values that can be used to graph f(x)=7/3 sinx.

Answer 1

To complete a table of values for the function \( f(x) = \frac{7}{3} \sin(x) \), we can evaluate \( f(x) \) at various standard angles. The sine function has known values at key angles (in radians): 0, \( \frac{\pi}{6} \), \( \frac{\pi}{4} \), \( \frac{\pi}{3} \), \( \frac{\pi}{2} \), \( \pi \), and so on.

Here’s a table of values for \( f(x) \):

| \( x \) | \( \sin(x) \) | \( f(x) = \frac{7}{3} \sin(x) \) |
|------------------|-------------------|-----------------------------------|
| 0 | 0 | 0 |
| \( \frac{\pi}{6} \) | \( \frac{1}{2} \) | \( \frac{7}{6} \) |
| \( \frac{\pi}{4} \) | \( \frac{\sqrt{2}}{2} \) | \( \frac{7\sqrt{2}}{6} \) |
| \( \frac{\pi}{3} \) | \( \frac{\sqrt{3}}{2} \) | \( \frac{7\sqrt{3}}{6} \) |
| \( \frac{\pi}{2} \) | 1 | \( \frac{7}{3} \) |
| \( \pi \) | 0 | 0 |
| \( \frac{3\pi}{2} \) | -1 | -\( \frac{7}{3} \) |
| \( 2\pi \) | 0 | 0 |

You can use these values to plot the graph of \( f(x) = \frac{7}{3} \sin(x) \). The sine function oscillates between -1 and 1, and the factor \( \frac{7}{3} \) scales this oscillation so that the output values range from \( -\frac{7}{3} \) to \( \frac{7}{3} \).