Question $3 e^{\operatorname{fin}} - 3 \sin (6 \pi x)$

Studdy Solution

STEP 1

1. The problem involves analyzing the expression $y = -3 \sin(6\pi x)$ .
2. The task is to understand the behavior of this function, likely focusing on its amplitude, period, and phase shift.
3. The expression $3 e^{\operatorname{fin}}$ seems unrelated to the sine function and might be a typographical error or irrelevant to the problem.

STEP 2

1. Identify the amplitude of the sine function.
2. Determine the period of the sine function.
3. Identify any phase shifts or vertical shifts.
4. Summarize the characteristics of the function.

STEP 3

Identify the amplitude of the sine function:
The amplitude of a sine function $y = a \sin(bx + c) + d$ is given by the absolute value of the coefficient $a$ . In this case, the function is $y = -3 \sin(6\pi x)$ .
$\text{Amplitude} = |-3| = 3$

STEP 4

Determine the period of the sine function:
The period of a sine function $y = a \sin(bx + c) + d$ is given by $\frac{2\pi}{|b|}$ . Here, $b = 6\pi$ .
$\text{Period} = \frac{2\pi}{6\pi} = \frac{1}{3}$

STEP 5

Identify any phase shifts or vertical shifts:
In the function $y = -3 \sin(6\pi x)$ , there is no horizontal shift ( $c = 0$ ) or vertical shift ( $d = 0$ ). Therefore, there are no phase shifts or vertical shifts.

STEP 6

Summarize the characteristics of the function:
- Amplitude: 3 - Period: $\frac{1}{3}$ - Phase Shift: None - Vertical Shift: None
The function $y = -3 \sin(6\pi x)$ oscillates with an amplitude of 3 and a period of $\frac{1}{3}$ , with no phase or vertical shifts.

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