the cartesian coordinates of a point are given (1,-3) find the polar coordinates `(r, theta)` where `r gt0` , `0<=theta<2pi` 

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Since the point (1,-3) is in the fourth quadrant, we can find the angle `theta` using the right angled triangle with sides 1, 3 and hypotenuse `sqrt{1+9}=sqrt10` .  The angle is going to then by (using the CAST rule)

`theta = 2pi - tan^{-1}(3/1)approx 5.03`

The value of r is the hypotenuse of the right angled-triangle, so `r=sqrt10` .

This means that the polar coordinates are `(r, theta)=(sqrt10, 5.03)` .

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial