Chapter 7: Additional Applications of Integration
Section 7.1: Polar Coordinates
Convert the Cartesian point −2,3 to polar coordinates.
The point −2,3 is in the second quadrant of the Cartesian plane where arctany,x and arctany/x do not agree. Hence, the formulas on the right in Table 7.1.1, modified to use the two-argument arctangent function are applied directly in Maple.
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 digits2.1588
Note that the naive calculation θ=arctan3/−2 gives θ≐−0.98, an angle in the fourth quadrant. Changing coordinates should not change the location of the point in the Cartesian plane. Hence, it is essential to use the two-argument arctangent function in this calculation.
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