Converting rectangular to polar

  • Thread starter kElect
  • Start date
  • #1
kElect
20
0

Homework Statement


How do you convert the rectangular coordinate points (1, -2) to polar form?

note: rectangular is (x,y) polar is (r, theta)


Homework Equations


r^2 = x^2 + y^2 , x = rcos(theta) , y = rsin(theta) , tan(theta) = y/x


The Attempt at a Solution


So basically, I tried getting it to polar form by first finding the radius. This part was easy since all I had to do was to plug it into the first equation.

r^2 = (1)^2 + (-2)^2
= sqrt(5)

Next, I tried getting theta by getting tan(theta).

tan(theta) = -2/1

Here is where the problem came in. When I tried putting this onto the unit circle, I didn't get any recognizable triangles(such as the 45-45 right triangle or the 30-60-90 right triangle).

So how would I find theta?(without using calculator)
 
Last edited:

Answers and Replies

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

Homework Statement


How do you convert the rectangular coordinate points (1, -2) to polar form?

note: rectangular is (x,y) polar is (r, theta)


Homework Equations


r^2 = x^2 + y^2 , x = rcos(theta) , y = rsin(theta) , tan(theta) = y/x


The Attempt at a Solution


So basically, I tried getting it to polar form by first finding the radius. This part was easy since all I had to do was to plug it into the first equation.

r^2 = (1)^2 + (-2)^2
= sqrt(5)

Next, I tried getting theta by getting tan(theta).

tan(theta) = -2/1

Here is where the problem came in. When I tried putting this onto the unit circle, I didn't get any recognizable triangles(such as the 45-45 right triangle or the 30-60-90 right triangle).

So how would I find theta?(without using calculator)

You wouldn't. You could express it is Arctan(-2) since that is in the 4th quadrant but you will need a calculator or tables for a decimal answer.
 
  • #3
kElect
20
0
You wouldn't. You could express it is Arctan(-2) since that is in the 4th quadrant but you will need a calculator or tables for a decimal answer.

even using a calculator my answer comes out to be -63.435 as theta whereas the answer is -1.107.
 
  • #4
eumyang
Homework Helper
1,347
11
even using a calculator my answer comes out to be -63.435 as theta whereas the answer is -1.107.
That's because -63.435 is in degrees whereas -1.107 is in radians.
 
  • #5
kElect
20
0
That's because -63.435 is in degrees whereas -1.107 is in radians.

oh ty.

hmm, strange. professor said calculator wasn't necessary.
 
  • #6
eumyang
Homework Helper
1,347
11
I guess you could state your answer like this:
[itex]\left( \sqrt{5}, \arctan (-2) \right)[/itex]
(Fortunately, we can leave arctan (-2) as it is, ie. not add a multiple of pi, because θ is in Q IV.)
 

Suggested for: Converting rectangular to polar

Replies
9
Views
848
  • Last Post
Replies
7
Views
449
Replies
11
Views
868
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
1
Views
740
Replies
9
Views
2K
Replies
1
Views
1K
Replies
3
Views
1K
Replies
9
Views
2K
Replies
1
Views
1K
Top