Convert the polar equation to rectangular form.

  • Thread starter Lebombo
  • Start date
  • #1
Lebombo
144
0

Homework Statement



r = 3sin[itex]\theta[/itex]

since

x= rcos[itex]\theta[/itex]

x = 3sin[itex]\theta[/itex]cos[itex]\theta[/itex]

and since:

y = rsin[itex]\theta[/itex]

y = 3[itex]sin^2\theta[/itex]


Then I'm sort of stuck..
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,568
774

Homework Statement



r = 3sin[itex]\theta[/itex]

since

x= rcos[itex]\theta[/itex]

x = 3sin[itex]\theta[/itex]cos[itex]\theta[/itex]

and since:

y = rsin[itex]\theta[/itex]

y = 3[itex]sin^2\theta[/itex]


Then I'm sort of stuck..

You are making it way too difficult. Put ##\sin\theta =\frac y r## in your first equation then see if you can get an xy equation from that.
 
  • #3
Dick
Science Advisor
Homework Helper
26,263
621

Homework Statement



r = 3sin[itex]\theta[/itex]

since

x= rcos[itex]\theta[/itex]

x = 3sin[itex]\theta[/itex]cos[itex]\theta[/itex]

and since:

y = rsin[itex]\theta[/itex]

y = 3[itex]sin^2\theta[/itex]


Then I'm sort of stuck..

Try putting sinθ=y/r.
 
  • #4
Lebombo
144
0
You are making it way too difficult. Put ##\sin\theta =\frac y r## in your first equation then see if you can get an xy equation from that.


Like so:

r = 3sinθ becomes (r=3[itex]\frac{y}{r}[/itex])

= (r =[itex]\sqrt{3y}[/itex]) ?


or solving for y, (y = [itex]\frac{r^2}{3}[/itex])



or do you mean something like this:



([itex]\frac{y}{r} = sinθ [/itex]) becomes ([itex]\frac{y}{3sinθ} = sinθ[/itex])


= (y = 3sin[itex]^{2}θ[/itex])
 
  • #5
Dick
Science Advisor
Homework Helper
26,263
621
Like so:

r = 3sinθ becomes (r=3[itex]\frac{y}{r}[/itex])

= (r =[itex]\sqrt{3y}[/itex]) ?


or solving for y, (y = [itex]\frac{r^2}{3}[/itex])



or do you mean something like this:



([itex]\frac{y}{r} = sinθ [/itex]) becomes ([itex]\frac{y}{3sinθ} = sinθ[/itex])


= (y = 3sin[itex]^{2}θ[/itex])

You also want to use ##r^2=x^2+y^2##. You need to express both ##sin(\theta)## and r in terms of x and y. Try once more.
 

Suggested for: Convert the polar equation to rectangular form.

Replies
9
Views
540
Replies
1
Views
577
Replies
1
Views
686
Replies
23
Views
523
Replies
4
Views
254
Replies
24
Views
421
  • Last Post
Replies
1
Views
387
Replies
3
Views
398
  • Last Post
Replies
3
Views
791
Replies
37
Views
2K
Top