# What is the amplitude, period, phase shift and vertical displacement of y=sinx-1?

Dec 17, 2017

Amplitude $= 1$
Period $= 2 \pi$
Phase shift $= 0$
Vertical Displacement $= - 1$

#### Explanation:

Consider this skeletal equation:

$y = a \cdot \sin \left(b x - c\right) + d$

From $y = \sin \left(x\right) - 1$, we now that

• $a = 1$
• $b = 1$
• $c = 0$
• $d = - 1$

The a value is basically the amplitude , which is $1$ here.

Since

$\text{period} = \frac{2 \pi}{b}$

and the b value from the equation is $1$, you have

$\text{period" = (2pi) / 1 => "period} = 2 \pi$

^ (use $2 \pi$ if the equation is cos, sin, csc, or sec; use $\pi$ only if the equation is tan, or cot)

Since the c value is $0$, there is no phase shift (left or right).

Finally, the d value is $- 1$, which means the vertical displacement is $- 1$ (the graph shifts down 1).