AlexanderMikus460idn
Answered

Discover new information and get your questions answered with IDNLearn.com. Get comprehensive answers to all your questions from our network of experienced experts.

How do I convert Cartesian coordinates to polar coordinates?

Sagot :

Luanaidn
[tex]Solving\ right\ triangle\ with\ two\ known\ sides. \ Cartesian\ coordinates\\ tell \ us\ about\ those\ sides.\ Example:\\ Coordinates\ (a,b)\ sides:\ a\ and\ b. \\ \\\\ From\ Pythagorean\ theorem\ find\ third\ side:\\ r^2=a^2+b^2\\ r=\sqrt{a^2+b^2}\\\\Using\ tangent\ function\ find\ angle:\\tan( \alpha )=\frac{b}{a}\\ \alpha =tan^{-1}\\\\Polar\ coordinates: \ (r, \alpha )[/tex]
AL2006idn
The Cartesian coordinates of a point are (x, y).
'x' and 'y'are both distances.

The polar coordinates of the same point are  (R, A).
'R' is a distance.  'A' is an angle.

How to find 'R' and 'A' when you know 'x' and 'y' :

R = distance of the point from the origin = square root of (x² + y²)

A = angle clockwise from the x-axis to the point = angle whose tangent is (y/x)

=====================================

If you HAVE the polar coordinates and you want to find the Cartesian ones,
then do it like this:

You have  (R, A) .

You want to find 'x' and 'y' .

x = R cos(A)

y = R sin(A)
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.