Well, 12,000 + 2000 / 2 = 7,000, yes?
Therefore from 7000 it is 5000 to 12000, and 5000 to 2000. So the amplitude is 5000.
I have already figured that out correctly, I believe....
The period is over the course of a year. There are about 52 weeks in a year.
Would I say that my period is 52? Or is it 360/52? I apologize in advance, it has been a while since sinusoidal functions.
I'm leaning more towards 52 being written in the equation, however.
Yes, the period is 52.
Remember that the period is given by .
So now solve for .
Also, how much of a horizontal translation has there been? Remember that a regular sine function begins at the origin.
360/52 = 6.9
Horizontal translations are something I have always been pretty dreadful at, and something I need a lot of practice with. I will hazard a guess, however...
If the max starts at week 4, and the min at week 30, and a sine function always starts at the origin, then there has been a horizontal shift 30 to the right?
So x - 30 ?
First, if you have trigonometric FUNCTIONS or GRAPHS, they are always measured in RADIANS.
So solve the equation for .
You should find that .
So now you have
You also have some points that you know lie on the graph, namely and .
So, let and equal some of these values.
So this means there has been a horizontal translation of units to the left.
And now, finally, your function is
My apologies. We haven't been taught radians yet--that's grade 12 here in Canada--though I understand your equations. However we will not be asked to use radians on any sort of test situation, so I would like to make sure I am getting the same answer in the 'correct' format for my course.
So in non-radian-speak, we have...
pt. (4, 12000)
12000 = 5000sin [6.9(4) - d] + 7000
5000 = 5000sin (27.6 - d)
1 = sin (27.6 - d)
arcsin (1) = 27.6 - d
90 - 27.6 = d
d = 62.4
Therefore the equation is ...
y = 5000sin (6.9x - 62.4) + 7000 ?
Looks good to me. However, I would be asking your teachers why you are in Year 12 and have not been taught Radian Measure, when it should have been taught in Year 10. Very sloppy of them...