## haleyelizabeth2017 one year ago In Buenos Aires, Argentina, the average monthly temperature is highest in January and lowest in July, ranging from 83 degrees Fahrenheit to 57 degrees Fahrenheit. Write a cosine function that models the change in temperature according to the month of the year. -How can you find the amplitude? -What part of the problem describes the length of the cycles?

1. haleyelizabeth2017

I got the amplitude....it's 13, but I'm not sure about the rest. Is it 70+13 cos ____ because 70 is where the middle of the graph is....

2. jim_thompson5910

13 is definitely the amplitude and y = 70 is the midline

3. jim_thompson5910

what is the period or length of each cycle?

4. haleyelizabeth2017

erm...not sure in this case....uno momento

5. haleyelizabeth2017

$$\pi/6$$ because there are 6 months in between January and July, which are the min and max values.

6. jim_thompson5910

well the period is actually 12 months since things repeat themselves each season (more or less) so B = 2pi/T B = 2pi/12 B = pi/6 so you have the pi/6 correct but pi/6 isn't the period. It's the coefficient for the t value

7. haleyelizabeth2017

Oh!

8. jim_thompson5910

So the function is $\Large y = 70+13\cos\left(\frac{\pi}{6}t\right)$ y = average temperature at month t

9. haleyelizabeth2017

Ah...I think we missed something...in the back of the book, it says that $$\frac{\pi}{6}$$ is the coefficient for (x-1), where x is the month of the year. I have to explain everything I do and it's my last question...any idea how they got that?

10. jim_thompson5910

the (x-1), instead of just x, is to allow x to start at 1 instead of 0 notice how x-1 = 0 when x = 1

11. jim_thompson5910

$\Large y = 70+13\cos\left(\frac{\pi}{6}x\right) ... \text{ x starts at x = 0}$ $\Large y = 70+13\cos\left(\frac{\pi}{6}(x-1)\right) ... \text{ x starts at x = 1}$ x = month number y = avg temp

12. haleyelizabeth2017

Oh! Duh! *face palm*

13. haleyelizabeth2017

Again, thank you very much. You're a lot of help lol

14. jim_thompson5910

you're welcome