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p3

sketch the curve:

x = 3cost y = 3sint

I just converted it into cartesian and then sketched that, is that right? Can someone post a pic of what it would look like(using one of those curve sketching programs) cheers.
Reply 1
Avatar for Fermat
Fermat
8
serious stuff
sketch the curve:

x = 3cost y = 3sint

I just converted it into cartesian and then sketched that, is that right? Can someone post a pic of what it would look like(using one of those curve sketching programs) cheers.

Those eqns are the standard parametric eqns of a circle, centre the origin, of radius 3. Think of t as theta, an angle.
Look at the diagram attached. You have a circle with a point P on the circle. The x-coordinate and y-coordinate are given by,

x = OQ = OP.cosø
y = PQ = OP.sinø

OP is the radius of the circle, so you can put r=OP and write the parametric eqns as,

x = r.cosø
y = r.sinø

Bonus Material
=========
If it had been an ellipse, cutting the x-axis at a and the y-axis at b, then the parametric eqns for an ellipse would be,

x = a.cosø
y = b.sinø

giving,

x²/a² + y²/b² = 1
===========
Parametric eqns.gif10.1KB
Reply 2
Avatar for Hoofbeat
Hoofbeat
14
Hey Fermat, what graph drawing program do you ue or recommend? I find graph drawing quite hard and have downloaded a 30day trial of Graph FAWM and have found that since I've been using it my ability has improved and so now I am thinking of investing in a program ready for University. Thanks :smile:
Reply 3
Avatar for Fermat
Fermat
8
Hoofbeat
Hey Fermat, what graph drawing program do you ue or recommend? I find graph drawing quite hard and have downloaded a 30day trial of Graph FAWM and have found that since I've been using it my ability has improved and so now I am thinking of investing in a program ready for University. Thanks :smile:

I use Adobe Photo Deluxe, which is great for every thing except curves - circles, ellipse, parabolas - any curved shape.
To get around that I now use a program called DrawPlus 4.0, which is an old Serif program.
You can download it free from ZDnet downloads
It's a bit finicky though. You can't save files as type .gif for example, you have to "export" them first. Other than that, it's not bad.
Fermat
I use Adobe Photo Deluxe, which is great for every thing except curves - circles, ellipse, parabolas - any curved shape.
To get around that I now use a program called DrawPlus 4.0, which is an old Serif program.
You can download it free from ZDnet downloads
It's a bit finicky though. You can't save files as type .gif for example, you have to "export" them first. Other than that, it's not bad.


i tried to install that program but it doesnt work
Reply 5
Avatar for serious stuff
serious stuff
OP
Whats wrong with coverting it to cartesian and then sketching that?
Reply 6
Avatar for Fermat
Fermat
8
serious stuff
Whats wrong with coverting it to cartesian and then sketching that?

Nothing!
You had,

x=3cost
y=3sint

If you square both sides and add them together you get,

x² + y² = 3²

which is the cartesian form (standard) of a circle, centre the origin, of radius 3.

I was simply pointing out, for those who might not recognise them, that those eqns were the standard parametrric eqns of a circle - knowing which, you can immediately see that what you have is a circle , centre the origin, of radius 3 - and so draw it straight away.
Reply 7
Avatar for Fermat
Fermat
8
tammypotato
i tried to install that program but it doesnt work

Do you mean you didn't get it installed, or you couldn't get it to give you any circles etc.?
If the latter was the problem, then I had the same one!
Use the shape templates to draw a circle/ellipse. Now right-click on the red colour and click on "edit fill colour". Change the colour to white. Now alter the line size in the line info window on the rhs of the work screen.
Reply 8
Avatar for serious stuff
serious stuff
OP
Fermat
Nothing!
You had,

x=3cost
y=3sint

If you square both sides and add them together you get,

x² + y² = 3²

which is the cartesian form (standard) of a circle, centre the origin, of radius 3.

I was simply pointing out, for those who might not recognise them, that those eqns were the standard parametrric eqns of a circle - knowing which, you can immediately see that what you have is a circle , centre the origin, of radius 3 - and so draw it straight away.


OK cool!

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