Question

Sales of ski equipment varies through the year from highs in January & December of $20 million, to a low in June of $2 million. Write a trigonometric function that describes this cycle. Calculate the expected sales for April.

I think I got the first part:
9cos(pi/6) + 11

I am just not sure how to calculate expected sales for April?

Answer 1

Your "function" contains no variables!
don't you mean

y = 9cos(pi/6)t + 11 ??

so if June corresponds with t=6 and Dec corresponds with t = 12
then April would match with t = 4
and y = 9cos(4pi/6) + 11
= 6.5

BTW, January does not seem to fit into the cycle. How can the max be in Dec and in Jan ?

Answer 2

A function generally implies the inclusion of one or more independent variables, which in this case, is t that represents the month.

So you'd need a function that has a cycle of 12 months, a maximum of 20 and a minimum of 2.

The choice of cosine is excellent.

The multiplicative constant of 9 and the additive constant of 11 is also correct.

So if you write the function as
S(t) = 9cos(pi*t/6) + 11
where t=0 to 12. (0 for the beginning of January, 12 for the end of december).
So S(0)=S(12)=20, and S(6)=2.

Try to figure out the sales for April (fourth month of the year).

Answer 3

I think you mean

9 cos (pi * x /6)

where x is the month number 0 through 11. And very neat that snswer is. It provides a low of 2 and a high of 20.

Mind you, you might want to mention that your actual answer is:

1,000,000(9cos(pi/6) + 11)

or

10^6(9cos(pi * x/6) + 11)

to make up that factor of a million.

So what about April? That's month 3 in the 0-11 sequence, so its value would be

10^6(9cos(pi * x/6) + 11)

or 11 million.

Answer 4

Oh yeah, I forgot to put the 'x' into my equation. I just plugged in the 4 where the x should be and got 6.5, or as it applies here, 6.5 million. Hope that's right. Thank you all! :)

Answer 5

yeah part exams library go there Pre-Calculus exam