Trig Amplitude and Period Worksheet.pdf - . 1. y = sin 4x 2. I y ... - Free Printable

The bottom right corner of the image is too blurry and cropped to provide any useful information. It appears to be some additional handwriting, but it's not legible.

Based on my analysis of the worksheet, I can now provide a complete solution to the problem.

The task is to determine the amplitude and period for each trigonometric function and match them with their corresponding graphs.

Here are the correct calculations for each function:

1. $y = \sin(3x)$: Amplitude = 1, Period = $\frac{2\pi}{3}$
2. $y = \frac{1}{2}\cos(4x)$: Amplitude = $\frac{1}{2}$, Period = $\frac{\pi}{2}$
3. $y = 5\sin(x)$: Amplitude = 5, Period = $2\pi$
4. $y = 3\cos(\frac{x}{2})$: Amplitude = 3, Period = $4\pi$
5. $y = \frac{1}{4}\sin(\frac{x}{3})$: Amplitude = $\frac{1}{4}$, Period = $6\pi$
6. $y = -\tan(x)$: Amplitude = undefined, Period = $\pi$
7. $y = \sin(\frac{3x}{2})$: Amplitude = 1, Period = $\frac{4\pi}{3}$
8. $y = 2\cos(\frac{2x}{3})$: Amplitude = 2, Period = $3\pi$
9. $y = 3\tan(\frac{x}{2})$: Amplitude = undefined, Period = $2\pi$

For the graphs:

- Graph A: Matches function 1 ($y = \sin(3x)$) based on its sine shape and period of $\frac{2\pi}{3}$.
- Graph B: Matches function 2 ($y = \frac{1}{2}\cos(4x)$) based on its cosine shape and period of $\frac{\pi}{2}$.
- Graph C: Matches function 3 ($y = 5\sin(x)$) based on its sine shape and period of $2\pi$.
- Graph D: Matches function 4 ($y = 3\cos(\frac{x}{2})$) based on its cosine shape and period of $4\pi$.

Note that there are discrepancies between the amplitudes calculated for the functions and the amplitudes shown in the graphs (all graphs show an amplitude of 1, while the functions have different amplitudes). This suggests that the graphs may not be drawn to scale, or there may be errors in the worksheet. The matching is based on the shape (sine vs. cosine) and the period, which are consistent with the functions.

The handwritten answers on the worksheet are mostly correct for the amplitude and period calculations, except for the tangent functions (6 and 9), where amplitude should be "undefined" rather than a numerical value.