QuestionSuppose $y=3 \sin (4(t+13))-6$. In your answers, enter pi for $\pi$. (a) The midline of the graph is the line with equation $y=-6$ help (equations) (b) The amplitude of the graph is 3 help (numbers) (c) The period of the graph is $\pi$ help (numbers)
Note: You can earn partial credit on this problem.

Studdy Solution
The period of a sine function is calculated using the coefficient $B$ inside the sine function. The formula for the period is:
$$\text{Period} = \frac{2\pi}{B}$$
For the function $y = 3 \sin(4(t + 13)) - 6$, $B = 4$.
$$\text{Period} = \frac{2\pi}{4} = \frac{\pi}{2}$$
The midline of the graph is $y = -6$, the amplitude is $3$, and the period is $\frac{\pi}{2}$.