Picture by deviantart.com user =NNBTK

The Kirby Plan

This is what we need to do…

1. We have decided on a target, Kirby, and a method of attack, our evil demon frog, all that’s left is figuring out WHEN to attack. Kirby needs to eat every 3 hours, for some reason he NEVER deviates from this pattern. Kirby fills up at a constant rate for 1.5 hours until he feels full. We are going to rate Kirby’s hunger on a scale from 1-10, 1 being the hungriest and 10 being when he is the fullest. Kirby first starts to eat at 1:00am.

A. Sketch a sinusoidal graph of Kirby’s eating habitsB. Write a sine and cosine equation for the graphC. We plan to attack Kirby when he’s at the park at 2:00pm. He can’t

seem to fight with much gusto if his fullness is above 8. i. Is 2:00pm a good time to attack?ii. What is a good time near 2:00pm to attack?

It’s graphing time!

• Don’t panic! Let’s take some important information from the question!

• Kirby needs to eat every 3 hours.3 hours is our period!

• Rate Kirby’s hunger on a scale from 1-10.1 is our min and 10 is our max!

• Kirby first starts to eat at 1:00am.1:00am is going to be our starting point!

Using what we learned in the last slide let’s make our graph!

The Eating Curve

NOTE: we are using the 24 hour clock for our x-axis (:

Sinusoidal axis

Period

Parts of the Equation!Parameter What is it?

A- amplitude This is the distance from the minimum or maximum to the sinusoidal axis.

B- determines It is the distance along the x-axis required period to make one wave. The period is equal to

C: Phase shift This determines the horizontal shift of the graph.

D: Vertical shift It determines the sinusoidal axis.

f(x)= Asin B(x- C) +Dg(x)= Acos B(x- C)+ D

2π3

It’s Equation time!

SinA: 4.5B: 3 So our sin equation isC: 1.75 f(Kirby)= 4.5sin (x- 1.75) + 5.5D: 5.5

2π3

NOTE: Make sure your calculator is in radians! NOT degrees! Otherwise you’ll end up with some wonky answers!

Now let’s do cosine!

CosA: -4.5B:3 So our cosine equation is C: 1 g(Kirby)= -4.5cos (x-1) +5.5D: 5.5

2π3

2:00, good or bad time to attack?

NOTE: We are using the 24 hour clock. 2:00pm is the equivalent of 14:00 hours.

Let’s try using our cosine equation to confirm!

So how do we figure out a good time to attack?

1. Write down your equation.

2. Let (x- 1.75) because it makes our equations easier to work with.

3. Re write the equation using θ.

4. Add -5.5 to both sides of your equation.

5. Divide both sides of the equations by 2.5.

6. Find the inverse sin of , and were done! Or are we…

59

θ= 2π3

Remember θ?

7. Convert θ back to the original value.

8. Now solve for x!

Lets see if we get the same answer with cosine!

Now let’s turn 2.03124 into TIME!

2.03124 (60)= 121.8744 min

It’s common sense time!There are 2 hours in 120 minutes, and 1.78 minutes left over. So that means we should attack at approximately 2:02 am.

So When Do We Attack??

02:02 14:02How did we do that?!

Well minions the answer to that is quite simple.

Our period is 3 hours, so we added 12 (which is a multiple of 3) to 02:02 to arrive at 14:02.

TOA (time of attack)= 14:02

Now that have all the math out of the way it’s time for us to get ready to attack!

SAY GOODBYE KIRBY!