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

x: 0, pi/2, pi 3pi/2, 2pi
f(x) = 7/3sinx:

1 answer

To complete the table of values for the function \( f(x) = \frac{7}{3} \sin x \) at the specified x-values, we will calculate \( f(x) \) at each given value of \( x \):

  1. For \( x = 0 \): \[ f(0) = \frac{7}{3} \sin(0) = \frac{7}{3} \cdot 0 = 0 \]

  2. For \( x = \frac{\pi}{2} \): \[ f\left(\frac{\pi}{2}\right) = \frac{7}{3} \sin\left(\frac{\pi}{2}\right) = \frac{7}{3} \cdot 1 = \frac{7}{3} \]

  3. For \( x = \pi \): \[ f(\pi) = \frac{7}{3} \sin(\pi) = \frac{7}{3} \cdot 0 = 0 \]

  4. For \( x = \frac{3\pi}{2} \): \[ f\left(\frac{3\pi}{2}\right) = \frac{7}{3} \sin\left(\frac{3\pi}{2}\right) = \frac{7}{3} \cdot (-1) = -\frac{7}{3} \]

  5. For \( x = 2\pi \): \[ f(2\pi) = \frac{7}{3} \sin(2\pi) = \frac{7}{3} \cdot 0 = 0 \]

Now we can summarize the completed table of values:

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

This table provides the necessary values to graph the function \( f(x) = \frac{7}{3} \sin x \) over one complete period.