Polar collaborates start with rectangle-shaped coordinates

Rectangular coordinates, or cartesian coordinates, come in the form ???(x,y)???.

It’s straightforward to remember that they’re referred to as rectangular coordinates, due to the fact that if you begin at the origin and move first to the ???x???-coordinate, and then to the ???y???-coordinate, your route is a horizontal line, adhered to by a vertical line, which kind two political parties of a rectangle.

You are watching: Plot the point whose polar coordinates are given. then find the cartesian coordinates of the point.



Polar coordinates, ~ above the other hand, come in the form ???(r, heta)???. Instead of relocating out native the beginning using horizontal and also vertical lines, we instead pick the edge ??? heta???, i beg your pardon is the direction, and then move out from the beginning a certain distance ???r???.


Rectangular to polar

To transform rectangular coordinates to polar coordinates, we’ll use the switch formulas


???x=rcos heta???

???y=rsin heta???

We’ll begin by plugging the ???x??? and ???y??? worths from the rectangular allude into the left next of ???x^2+y^2=r^2???, and also we’ll obtain a worth for ???r???.

Then fine use

???r??? and also the ???x???-value and plug them right into ???x=rcos heta???

???r??? and the ???y???-value and plug them into ???y=rsin heta???.

The value of ??? heta??? that turns out to be a solution to both equations is the value of ??? heta??? we should use in our converted polar point.

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Polar to rectangular

To transform polar works with to rectangle-shaped coordinates, we’ll use the counter formulas

???x=rcos heta???

???y=rsin heta???

All we have to do is take the values of ???r??? and ??? heta??? from the polar point, plug them into the right sides of this conversion formulas, and solve for ???x??? and ???y???, the worths we need for the identical rectangular name: coordinates point.