Question$$-5 \sin (0.5 x+1)$$ amplitude: a period: d horizontal shift: $\qquad$

Studdy Solution
The horizontal shift (phase shift) of a sine function $a \sin(bx + c)$ is calculated using the formula:
$$\text{Horizontal Shift} = -\frac{c}{b}$$
For the function $-5 \sin(0.5x + 1)$, the constant $c$ is $1$ and $b$ is $0.5$. Thus, the horizontal shift is:
$$\text{Horizontal Shift} = -\frac{1}{0.5} = -2$$
The amplitude is $\boxed{5}$, the period is $\boxed{4\pi}$, and the horizontal shift is $\boxed{-2}$.