How do you graph and list the amplitude, period, phase shift for $y = - sin (π x + 1) - 2$ $y=-sin(pix+1)-2$ ?

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How do you graph and list the amplitude, period, phase shift for $y = - sin (π x + 1) - 2$ $y=-sin(pix+1)-2$ ?

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Answer 1 · 2018-03-17T15:16:21

I use the online graphing calculator Desmos. You merely enter the function $y = - sin (π x + 1) - 2$ $y=-sin(pix+1)-2$ and it produces very nice graphs that can be exported:

![www.desmos.com/calculator]( useruploads.socratic.org )

This is a good reference for Graphing Trigonometric Functions

When given a sine function of the form:

$y = A sin (B x + C) + D$ $y = Asin(Bx+C)+D$

The amplitude is $| A |$ $|A|$

In the case of, $y = - sin (π x + 1) - 2$ $y=-sin(pix+1)-2$ , the amplitude is $| - 1 | = 1$ $|-1| = 1$

The period is:

$τ = \frac{2 π}{| B |}$ $tau = (2pi)/|B|$

$τ = \frac{2 π}{π}$ $tau = (2pi)/pi$

$τ = 2$ $tau = 2$

The phase shift is:

$ϕ = - \frac{C}{B}$ $phi = -C/B$

$ϕ = - \frac{1}{π}$ $phi = -1/pi$

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How do you graph and list the amplitude, period, phase shift for $y = - sin (π x + 1) - 2$ $y=-sin(pix+1)-2$ ?

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How do you graph and list the amplitude, period, phase shift for y=−sin(πx+1)−2y=-sin(pix+1)-2?

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How do you graph and list the amplitude, period, phase shift for $y = - sin (π x + 1) - 2$ $y=-sin(pix+1)-2$ ?