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Expert: - 11/20/2009


Question

#2 Trig
Problem #2 - I'm having problems doing this in reverse.  Could use some help.  Thanks!

Answer
Questioner: Jill
Country: United States
Category: Advanced Math
Private: No
Subject: Trigonometry
Question:

#2 Trig - I'm having problems doing this in reverse.  Could use some

help.  Thanks!  
......................................
Hi, Jill,

You want a function:

y = A sin-or-cos(b(x + phase)) + offset

I can't say your picture is totally clear, but we can draw some

conclusions:

I will assume it goes up to +4 and down to -2.  (That isn't clear, but

it's the best I can do.)

So the average value is +1, and FROM THAT, it goes up and down 3.  So it

has:
Amplitude = 3.
Offset = 1.

So we are up to:

y = 3 sin-or-cos(b(x - phase)) + 1

Now it crosses the x-axis at just to the right of -1 and just to the

right of +5.  Looks like a period of 6, just a bit less than 2pi.  Of

course, if I am misreading the graph, maybe it is exactly 2pi, then the

frequency (b) is 1.

The rule is:  b[period] = 2pi

So 6b = 2pi,  b = pi/3.

So we are up to:

y = 3 sin-or-cos(pi/3 (x - phase)) + 1

Now if we choose sine, we see the curve 'starting' at x = -1/2.

'Starting' means crossing its 'center line', not necessarily y = 0. In

this case it's  y = 1.  So the phase is -1/2 and we have:

y = 3 sin(pi/3 (x PLUS 1/2)) + 1

That should do it.  

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

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I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

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