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Section 12.12 : Cylindrical Coordinates
2. Convert the Cartesian coordinates for into Cylindrical coordinates.
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Start SolutionFrom the point we’re given we have,
So, we already have the coordinate for the Cylindrical coordinates.
Show Step 2Remember as well that for and we’re going to do the same conversion work as we did in converting a Cartesian point into Polar coordinates.
So, getting is easy.
Show Step 3Finally, we need to get .
If we look at the three dimensional coordinate system from above we can see that is in the first quadrant and is in the third quadrant. Likewise, from our and coordinates the point is in the third quadrant (as we look at the point from above).
This in turn means that we need to use for our point.
The Cylindrical coordinates are then,