Homework Help Forum: Pre-Calculus

Posted by Natalie on Thursday, October 29, 2009 at 7:46pm.

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?

• Pre-Calculus - Reiny, Thursday, October 29, 2009 at 9:07pm

  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 ?

  
  

• Pre-Calculus - MathMate, Thursday, October 29, 2009 at 9:13pm

  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).

  
  

• Pre-Calculus - jim, Thursday, October 29, 2009 at 9:13pm

  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.

  
  

• Pre-Calculus - Natalie, Thursday, October 29, 2009 at 9:55pm

  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! :)

  
  

• Pre-Calculus - stephanie, Thursday, October 29, 2009 at 10:13pm

  yeah part exams library go there Pre-Calculus exam

  
  

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