I need help understanding the concept, starting with #46. I will post a picture.

Question

littlebird · Answer

attachment

littlebird · Answer

I'm using a graphing calculator.

kainui · Answer

Sure, do you know how to put your graphing calculator into parametric graphing mode?

littlebird · Answer

Yes

kainui · Answer

Perfect. So basically all you're doing here is looking each point made (x,y) for every t between 0 and 2pi.

So to give you a concrete example, it says:

x=5cos(t) and y=2sin(t) then if you plug in t=0 you get the point: (5cos0,2sin0) which is, (5,2).

Now you try plugging in any value of t, and then tell me what point you get from it. Just do a few and you'll start to see the curve emerge.

littlebird · Answer

What will this pattern tell me?

kainui · Answer

The pattern will just draw out a graph, just like y=x^2 draws out a parabola.

kainui · Answer

In this case, the graph will look like an ellipse.

littlebird · Answer

I saw the ellipse. Now what?

kainui · Answer

Since this fails the vertical line test, we can't normally graph this function unless we use parametric graphing. That's sort of the power of parametric graphing. Now you've graphed it, unless you have any specific questions it looks like you just do parts A and B like they describe. I'm here if you have more questions though.

littlebird · Answer

How do I identify the initial and terminal points?

kainui · Answer

That's just a fancy way of saying beginning and ending. Just plug in the first and last points that t can be into your graph. Remember,$$0 \le t \le 2 \pi$$

littlebird · Answer

I understand part a now. How do I find a Cartesian equation?

kainui · Answer

So basically Cartesian is just the fancy way to call the normal way of graphing y=mx+b and that kind of stuff where y is a function of x.

So in order to do that, you just need to see that you have:

y=2sint and x=5cost

So you have a y= something but it's in terms of t. You can now solve for t from the x= equation and plug that into the y= to get an equation of y in terms of x. Does that make sense?

littlebird · Answer

Makes sense, but how should I start solving for t?

kainui · Answer

x=2sint. Just use that and solve normally with algebra until you get t= something. Also, remember that arcsine is the opposite of sine just like the square root is the opposite of squaring a number.

littlebird · Answer

How do I separate the sin and T? By dividing?