For y = -2 cos(3x + π), find the amplitude, the period (to 3 decimal places) and the range…

Step 1. Amplitude. $|-2| = 2$.

Step 2. Period. $\dfrac{2\pi}{3} \approx 2.094$.

Step 3. Range. The middle line is $y = 0$, so the range is $[-2, 2]$.

Step 4. The same graph. The point at $\theta + \pi$ is opposite the point at $\theta$, so $\cos(\theta + \pi) = -\cos\theta$. With $\theta = 3x$, $y = -2 \times (-\cos 3x) = 2\cos 3x$.