What is the amplitude, period, phase shift and vertical displacement of $y = 2 sin (2 x - 4) - 1$ $y=2sin(2x-4)-1$ ?

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Answer 1 · 2018-02-20T01:42:54

See below.

When $y = a sin (b x + c) + d$ $y = asin(bx+c)+d$ ,

amplitude = $| a |$ $|a|$
period = $\frac{2 π}{b}$ $(2pi)/b$
phase shift = $- \frac{c}{b}$ $-c/b$
vertical shift = $d$ $d$

(This list is the kind of thing that you have to memorize.)

Therefore, when $y = 2 sin (2 x - 4) - 1$ $y=2sin(2x-4)-1$ ,

amplitude = 2
period = $\frac{2 π}{2}$ $(2pi)/2$ = $π$ $pi$
phase shift = $- (- \frac{4}{2})$ $-(-4/2)$ = 2
vertical shift = -1

What is the amplitude, period, phase shift and vertical displacement of y=2sin(2x-4)-1y=2sin(2x−4)−1y=2sin(2x-4)-1?