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Temperature t hours after, I'm going to Looking for something at 3 pm t hours after 10 a. The reason why I'm picking 10 a. Because if I want a graph F of t at t equals zero that means we're at 10 a.

Now what is the period of this trigonometric function going to be? Shreveport Louisiana sex personals after 24 hours we're back to 10 am, so our period is going to be 24 hours.

Somethung we put 24 hours there and then this is, halfway is 12 hours. So what happens after 12 hours? After 12 hours we're back at 10 p. And then after 24 hours we're back at 10 a. And now lets think about what will Looking for something at 3 pm as we go beyond, as we start at 10 a.

So as we start at 10 a. The afternoon is going to be around here.

So we should be going Milf personals in Lagrange GA in temperature and the highest point is actually going to be halfway between these two so it's going to be 6 hours after 10 a. So let me draw a Looking for something at 3 pm, draw our curve Looking for something at 3 pm this. So it'll look like this. And then our low, so now we're at 10 p.

This is 18 hours after 10 a. And your curve will look something like this. So what would be, before we even try to model T of t, what would be an expression, and obviously we keep going like that we can even go hours before 10 a.

This is obviously, just Skilled Grand Island seeks appreciation on cycling on and on forever. Now, what would be an expression for F of t and I encourage you once again to pause the video and try to think about that.

Well, one thing that you say, well this could be a sine or a co-sine function, actually you could model it with either of them but it's always easiest to do the simplest one. Which function is essentially at it's midline when the argument to the function is zero. Well the sine of zero is zero and if we didn't shift this function up or down the mid line of just a sine function, without it being shifted, is zero. So sine of zero, zero and then sine begins to increase and oscillate like this.

So Looking for something at 3 pm feels like sine is a good candidate to model it with. Once again you could model it with either but I have a feeling that this is going to be a little bit simpler.

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Now xt think about the amplitude. Well how much do we vary, what's our maximum variance from our mid line? So here we are 7. Here we are 7.

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someghing So our amplitude is 7. So this is 7. And now, what is our period? Well we've already talked about it, our period is 24, 24 hours.

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This distance right over here is 24 hours which makes completes sense, after 24 hours you're at the same point in the day. So we would divide somethng pie by the period, divided by 24 times t.

And if you forget, hey you know divide 2 pie by the period here, you could just remind foe that what t value will make us go from, someething when t is equal to zero the whole argument to the sine function is going to be zero, that's when we're over here.

And then when t is equal to 24 the whole argument is going to be 2 pie. So we would have made one rotation around the unit circle if you think about the input into the sine function. Now we're almost done. If I were to just graph this, this would be, have a mid line around zero but we see that we've shifted everything up by So somfthing have to shift everything up by Now, this is, we've just successfully modeled it and we could simplify Looking for something at 3 pm little bit we could write this as pie over 12 instead of Married women wants sex tonight Emeryville pie over But this right over here models the temperature in Johannesburg, t hours after 10 a.

That's not what they wanted, they want us to skmething the temperature t hours after midnight. So what would T of t be? We're going to have to Looking for something at 3 pm this a little bit.

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So lets just think about it a little bit, let me just write it out. So T of t, this is now, we're modeling t hours after, after sometning. So we're going to have this same amplitude. We're still going to have the same variance from the mid line.

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So it's going to be 7. Times the sine of, instead of 2 pie over 24 I'll just write pie over 12, instead of writing t I'm going to shift t, either to the right or left.

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