Chapter 7: Additional Applications of Integration

Section 7.1: Polar Coordinates

Example 7.1.3

$$ Convert the polar point $\left(2\,3\right)$ to Cartesian coordinates. $$ Solution $$ For the calculus, there are no special tools in Maple for changing the coordinates of points. The simplest way to change a polar point to Cartesian coordinates is by direct application of the formulas on the left in Table 7.1.1. $$ •  Write the expression for $x$. •  Context Panel: Approximate≻5 (digits) $2 \cos \left(3\right)$$\stackrel{\text{at 5 digits}}{\to }$$-1.9800$ •  Write the expression for $y$. •  Context Panel: Approximate≻5 (digits) $2 \sin \left(3\right)$$\stackrel{\text{at 5 digits}}{\to }$$0.28224$ $$ Hence, the polar point $\left(2\,3\right)$ is the Cartesian point $\left(2 \cos \left(3\right)\,2 \sin \left(3\right)\right)\doteq \left(-1.98.0.28\right)$.

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