Question

Can someone help check these parametric equation graphs?

Answer 1

I just need to know if the equation matches up with the graph.

Answer 2

if i understand you correctly, i don't think they do, i'm afraid

https://i.gyazo.com/60e32fcfba3bd363105a538dd0cd5bac.png

for the first one, you can say that \(\sin^2 t = (\dfrac{x}{3})^{2/3}\) and \(cos^2 t = y^{2/3}\)

so \((\dfrac{x}{3})^{2/3} + y^{2/3} = 1\). you get that funny little blue thing in the middle. it's not a circle.

[for the second, i think it's called a rose and is best explained using complex numbers or polar. its like a point on a little circle that is rotating about its centre whilst also rotating about the origin following the locus of a larger circle. ignore that if it sounds gibberish.]

but go to desmos and work out how to graph parametric equations, and your life might be easier.

Answer 3

When I went on desmos and typed those equations in that's what it brought up.

Answer 4

nah, for the second one, it is plotting x and y separately, yes? so it is taking t as the independent variable in each and plotting x and y separately as dependent variables.

look at the left hand side of the link i have. in desmos, you do parameters by entering a single coordinate based on parameter t, and then you specify a range for that t. it then plots y and x over that range as ordered pair (x,y).

there's an example on there in the menu too on the LHS.

Answer 5

desmos may be great, but in the long run we need to be able to be able to graph parametric equations (or get a feel for their shapes) manually.

Note that there's a bit of confusion in your "x=3sin^3t" ... was that meant to be "three times the cube of sin t?"

Have you tried eliminating the parameter, t?

Answer 6

I'm on my school computer and they have gyazo blocked :(

Answer 7

Eliminating the parameter is the next lesson I have, so no I haven't done it yet.

Answer 8

Could you take advantage of the fact that (sin t)^2 + (cos t)^2=1?

Answer 9

@mathmale that is what i posted above. and yes it works for the first one, but that is a really poor way to get something plottable IMHO FWIW. it's kinda an inverse cycloid

i'd say you get it much more intuitively out of complex numbers. it becomes quite easy after a while, i just haven't done one in ages.

Answer 10

@IrishBoy123 : Apologies for duplicating your efforts. Thx for the insights shared.

Answer 11

@mathmale

i think the OP need to get on top of desmos. use it as an assistant, not to just get answers. that bit's important, i guess!!!

experiment with it. it is really an excellent way to build an intuition. even something like y\(y = a x^2 + bx + c\), with desmos sliders, it is really eye-opening!! to me at least.

good luck!!

Answer 12

@alexh107
if you're blocked from Gyazo currently, i can try sending that file to you from desmos

https://www.desmos.com/calculator/weycfkq13d

hope that helps you

Answer 13

Okay, that helps a lot. Thank you!

Answer 14

:p