Find a, b, and c...2

[nycmathguy]

Section 4.5

Question 72

We need to find the value of a, b, and c for the equation f(x) = a•sin (bx - c).

Let a = amplitude

So, a = 2.

Let b = period.

The period is the distance between two peaks or two troughs.

So, b = 4.

Let c = phase shift = 1

Our equation is f(x) = 2 sin(4x - 1).

You say?

 

[MathLover1]

amplitude: a=2
recall: When b=1, the graph has a period of (2pi)/1=2pi.

you have b=4
a period is 2pi/4=pi/2

c=3/2

f(x) = 2 sin((pi/2)x - 3/2)

 

[nycmathguy]

amplitude: a=2
recall: When b=1, the graph has a period of (2pi)/1=2pi.

you have b=4
a period is 2pi/4=pi/2

c=3/2

f(x) = 2 sin((pi/2)x - 3/2)

You said b = 1. What on the graph indicates that this is the value of b?

 

[MathLover1]

sorry, I said
you have b=4
a period is 2pi/4=pi/2
c=3/2

then I accidentally put f(x) = 2 sin((pi/2)x - 3/2) instead b=4
f(x) = 2 sin(4x - 3/2)

 

[nycmathguy]

sorry, I said
you have b=4
a period is 2pi/4=pi/2
c=3/2

then I accidentally put f(x) = 2 sin((pi/2)x - 3/2) instead b=4
f(x) = 2 sin(4x - 3/2)

Ok. I almost got it right. How do you find b?