Determine an equation for the curve.

[amy-lee]

FOr the half-wave design, determine an equation for the curve, assuming that the origin is at the point (0,0)

I'm confused on how to get the equation for the curve from the attached graph.

 

[wjm11]

FOr the half-wave design, determine an equation for the curve, assuming that the origin is at the point (0,0)

If this is a half wave, we can see that it’s centered on the line y = 7; hence the vertical displacement is 7.

We can also see that it has a peak at 11. Therefore the amplitude must be 11 – 7 = 4.

As for phase shift (horizontal displacement), one way to interpret this curve is to say it has been shifted 5 units to the left.

Notice also that the half wave spans from –5 to 5, a total of ten units. The period is twice that, 20 units.

You now have all the pieces of the puzzle. Can you proceed from here?

 

[Deleted member 4993]

In addition, knowing that maximum occurs at x = 0, you should be able to determine whether to consider a sine curve or a cosine curve. It really does not matter - just makes the problem a little simpler.

 

[amy-lee]

So then the equation should be:
y=4sinpi/10(x+5)+7 ??

 

[Deleted member 4993]

So then the equation should be:
y=4sinpi/10(x+5)+7 ??

You got it...

\(\displaystyle y\, = \, 7\, + \,4\cdot\sin{[\frac{\pi}{10}(x\, + \, 5)]}\)

or

\(\displaystyle y\, = \, 7\, + \,4\cdot\cos{[\frac{\pi}{10}(x)]}\)

Both the functions satisfy the given boundary conditions.