What do you mean by a "zero" value? You do not include a vertical shift term. The minimum of -5 indicates to me that
y = 5sin(b(x-c))
I assume your zero value is supposed to help define the period...
Find a trigonometric equation in the form y = a sin (b (x-c)) which has a minimum of (3, -5) and a zero value of (6, -1).
There is a graph with the minimum and the zero value labeled. It is wavy with suggests that it is a sin curve.
4 answers
What I don't understand about this problem is that what the letters mean?
I am sorry I forgot the + d at the end.
I am sorry I forgot the + d at the end.
ah! that makes all the difference!
Since the center line is at y = -1, the distance to the extremes is the amplitude. So, the amplitude is 4 and the vertical shift is -1. That means
y = 4sin(b(x-c))-1
since sin(0) = 0, that means y+1=0 at x=6, so the horizontal shift is 6
the distance from the zero value to the minimum is 3, so the period is 12.
Now the period of sin(kx) is 2π/k. That means k=π/6
y = 4sin(π/6 (x-6)) - 1
see the graph at
http://www.wolframalpha.com/input/?i=plot+y%3D4sin(%CF%80%2F6+(x-6))+-+1,+y%3D-1+for+0%3C%3Dx%3C%3D12
Since the center line is at y = -1, the distance to the extremes is the amplitude. So, the amplitude is 4 and the vertical shift is -1. That means
y = 4sin(b(x-c))-1
since sin(0) = 0, that means y+1=0 at x=6, so the horizontal shift is 6
the distance from the zero value to the minimum is 3, so the period is 12.
Now the period of sin(kx) is 2π/k. That means k=π/6
y = 4sin(π/6 (x-6)) - 1
see the graph at
http://www.wolframalpha.com/input/?i=plot+y%3D4sin(%CF%80%2F6+(x-6))+-+1,+y%3D-1+for+0%3C%3Dx%3C%3D12
Thank you so much Steve!