Chapter 7: Additional Applications of Integration
Section 7.1: Polar Coordinates
Example 7.1.1
Convert the Cartesian point 2,3 to polar coordinates.
Solution
Mathematical Solution
The point 2,3 is in the first quadrant of the Cartesian plane where arctany,x and arctany/x agree. Hence, the formulas on the right in Table 7.1.1 give
r=22+32=13
θ=arctan3,2=arctan3/2≐0.98 radians
Maple Solution
For the calculus, there are no special tools in Maple for changing the coordinates of points. The simplest way to change a Cartesian point to polar coordinates is by direct application of the formulas on the right in Table 7.1.1.
Write the expression for r.
Context Panel: Evaluate and Display Inline
22+32 = 13
Write the expression for θ.
Context Panel: Approximate≻5 (digits)
arctan3,2→at 5 digits0.98279
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