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

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Answer 1 · 2017-12-17T03:08:20

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

Consider this skeletal equation:

#y = a*sin(bx - c) + d#

From #y = sin(x) - 1#, we now that

#a = 1#

#b = 1#

#c = 0#

#d = -1#

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

Since

#"period" = (2pi) / b#

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

#"period" = (2pi) / 1 => "period" = 2pi#

^ (use #2pi# 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).