converting rectangular to polar

[kElect]

1. The problem statement, all variables and given/known data
How do you convert the rectangular coordinate points (1, -2) to polar form?

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


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


3. 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)

[LCKurtz]

1. The problem statement, all variables and given/known data
How do you convert the rectangular coordinate points (1, -2) to polar form?

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


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


3. 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.

[kElect]

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.

[eumyang]

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.

[kElect]

That's because -63.435 is in degrees whereas -1.107 is in radians.

oh ty.

hmm, strange. professor said calculator wasn't necessary.

[eumyang]

I guess you could state your answer like this:
\left( \sqrt{5}, \arctan (-2) \right)
(Fortunately, we can leave arctan (-2) as it is, ie. not add a multiple of pi, because θ is in Q IV.)