# Find a function that models the brightness of the star as a function of time (in days), t.A variable star is one whose brightness alternately increases and decreases. For one such star, the time...

Find a function that models the brightness of the star as a function of time (in days), *t.*

A variable star is one whose brightness alternately increases and decreases. For one such star, the time between periods of maximum brightness is 5.0 days, the average brightness (or magnitude) of the star is 4.6, and its brightness varies by ±0.35 magnitude. (Assume that at *t* = 0 the brightness of the star is 4.6 and that it is increasing.)

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### 1 Answer

A variable star is one whose brightness alternately increases and decreases. For one such star, the time between periods of maximum brightness is 5.0 days, the average brightness (or magnitude) of the star is 4.6, and its brightness varies by ±0.35 magnitude. (Assume that at *t* = 0 the brightness of the star is 4.6 and that it is increasing.)

Time to bring in the trig!

The period of the function must be 5 days. The amplitude must be 0.35. The function must be translated up 4.6 units.

So let's start with you regular sine graph

But how to change it from a period of 2pi to a period of 5? We want the function to "think" it's at 2pi when x is really at 5. So we just multiply x by 2pi/5.

`y=sin((2pi)/5x)`

Instead of squiggling between 1 and -1, we want our function to go from 0.35 to -0.35.

`y=0.35sin((2pi)/5x)`

Now shift it up 4.6 and we're done!

`y=0.35sin((2pi)/5 x)+4.6`