PRE-Calc Help: y = asin(bx + c) + d?

Ugh I have to do this in my class at my school also...

so... you probably already know this but...I'll go from the beginning just in case.

y=d asinb(x c)

d=the vertical shift a=the amplitude b=2pi/period c=the horizontal shift

it's usually easier to graph it out first. After that, you can figure everything out by using the graph:

here's a link to one I did in google drive: https://docs.google.com/spreadsheet/ccc?key=0Ajitl...

by taking the average of the minimum and the maximum: (90 51) /2 we get 70.5

so it shows that the vertical shift is 70.5

the amplitude is just the difference from the halfway point (70.5) to the maximum or minimum

90 - 70.5 = 19.5 so 19.5 is your amplitude.

the period is obviously over a year, or 12 months, so it's 2pi/ 12

so b is pi/6

in this case there is no horizontal shift because it starts from the minimum

so basically your final answer should be:

y= 70.5 19.5 sin pi/6x

you can check it by plugging it into a graphing calculator.

This turned out as practice for me as well... I hope it helped :)