## Not sure how to make this into a function.

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
CrazELuckK
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### Not sure how to make this into a function.

the problem is "You are told that the percentage of the viewable moon surface that is illuminated in the year 2013 is modeled by a trigonometric function. Let d represent the days since January 1, 2013. When d = 0, 100% of the viewable moon surface is illuminated. When d = 14.76 we have that 0% of the viewable moon surface is illuminated. When 0% is illuminated this is called a new moon."

"(a) Find a sine function V(d) to model this situation, where V is the percentage of the surface that is illuminated and d is the number of days since January 1,2013. Clearly show how you find the period, amplitude, horizontal shift, and midline of your function."

I know the basic y=Asin(Bx+C)+D where A is amplitude, B is period, C is horizontal shift and D is vertical shift, but i dont know what to plug in where :/

buddy
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Joined: Sun Feb 22, 2009 10:05 pm
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### Re: Not sure how to make this into a function.

You are told that the percentage of the viewable moon surface that is illuminated in the year 2013 is modeled by a trigonometric function. Let d represent the days since January 1, 2013. When d = 0, 100% of the viewable moon surface is illuminated. When d = 14.76 we have that 0% of the viewable moon surface is illuminated. When 0% is illuminated this is called a new moon.
The curve goes from 100% (the max) to 0% (the min) in 14.76 days. The cosine wave goes from 1 (the max) to -1 (the min) in the first half of its period. So do a cosine wave and use 0-100 as the range. Then the midline is halfway between and the amplitude gets you to the max/min numbers. Also 14.76 is half the period, so 2*14.76 is a whole period. Since they have you start at the max, you don't need any phase shift.