Write Cosine Function Given Maximum and Minimum

Algebra
Tutor: None Selected Time limit: 1 Day

Write a cosine function, f(x), such that on one period a local maximum is at (-pi/3, 1) followed by a local mnimum at (2pi/3, -7).  

Jun 3rd, 2015

Thank you for the opportunity to help you with your question!

Since the difference between maximum and minimum is 8, the amplitude is 4.

Since the local maximum is at -pi/3, you add pi/3 to the x value.

Since the difference in the x value of the maximum and minimum is pi, the period is 2pi.

Since the average between the maximum and minimum is -3, you add 3 to the y value.

This leaves you with the equation y = 4cos(x+pi/3) - 3

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 3rd, 2015

Would you please clarify as to why the period is 2pi? I can see the difference in the x value of the maximum and minimum is pi, but I don't know how you deduced that the period is twice as much? Thank you.

Jun 3rd, 2015

Since the difference between the maximum and the minimum is pi, the difference between the minimum and the next maximum is also pi. This means that the distance between any two maximums is 2pi. I hope this clears it up.

Jun 3rd, 2015

Also, in my book the formula for the COS function is given as f(x) = a cos b(x - h) + k. In your solution, we have calculated a, h, and k. However, we did not calculate 'b' and did not utilize the period. Can you explain that, as well? Thank you.

Jun 3rd, 2015

The equation should actually be f(x) = a cos (bx -h) + k. The normal period of a cosine graph is always 2pi, so in this case b = 1. You can show this through the equation y = cos(x). The period of this graph is 2pi and the b value is 1. 

Jun 3rd, 2015

Thanks a bunch!

Jun 3rd, 2015

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