Question

Complete the table of values that can be used to graph f(x)=−4cosx.(2 points)
This table displays given x-values, where the corresponding f(x)= - 4cos x values need to be calculated to complete the table.
x f(x)=−4cosx
0
π2
π
3π2
2π

Answer 1

To complete the table for the function \( f(x) = -4 \cos x \), we need to calculate \( f(x) \) at the given x-values. Here are the calculations for each value:

1. **When \( x = 0 \)**:
\[
f(0) = -4 \cos(0) = -4(1) = -4
\]

2. **When \( x = \frac{\pi}{2} \)**:
\[
f\left(\frac{\pi}{2}\right) = -4 \cos\left(\frac{\pi}{2}\right) = -4(0) = 0
\]

3. **When \( x = \pi \)**:
\[
f(\pi) = -4 \cos(\pi) = -4(-1) = 4
\]

4. **When \( x = \frac{3\pi}{2} \)**:
\[
f\left(\frac{3\pi}{2}\right) = -4 \cos\left(\frac{3\pi}{2}\right) = -4(0) = 0
\]

5. **When \( x = 2\pi \)**:
\[
f(2\pi) = -4 \cos(2\pi) = -4(1) = -4
\]

Now we can fill in the table with the calculated values:

| \( x \) | \( f(x) = -4 \cos x \) |
|-------------------|---------------------------|
| \( 0 \) | \( -4 \) |
| \( \frac{\pi}{2} \) | \( 0 \) |
| \( \pi \) | \( 4 \) |
| \( \frac{3\pi}{2} \) | \( 0 \) |
| \( 2\pi \) | \( -4 \) |

These values can now be used to graph the function \( f(x) = -4 \cos x \).