Unformatted text preview: at we’ve had practice converting representations of points between the rectangular and polar
coordinate systems, we now set about converting equations from one system to another. Just as
we’ve used equations in x and y to represent relations in rectangular coordinates, equations in the
variables r and θ represent relations in polar coordinates. We convert equations between the two
systems using Theorem 11.7 as the next example illustrates.
1. Convert each equation in rectangular coordinates into an equation in polar coordinates.
(a) (x − 3)2 + y 2 = 9 (b) y = −x (c) y = x2 2. Convert each equation in polar coordinates into an equation in rectangular coordinates.
(a) r = −3
5 See Example 10.6.5 in Section 10.6.3. (b) θ = 4π
3 (c) r = 1 − cos(θ) 790 Applications of Trigonometry Solution.
1. One strategy to convert an equation from rectangular to polar coordinates is to replace every
occurrence of x with r cos(θ) and every occurrence of y with r sin(θ) and use identities to
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