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Chapter 6: Problem 12

A point in polar coordinates is given. Convert the point to rectangular coordinates. $$(0,-\pi)$$

Short Answer

Expert verified
The point in rectangular coordinates is (0,0).

Step by step solution

01

Understanding the given point in polar coordinates

The point in polar coordinates is given as (0,-蟺). This tells us that the radial distance, 'r', is 0 and the angle, '胃', is -蟺.
02

Apply the conversion formulas

To convert the given polar coordinates to rectangular coordinates, we use the formulas for 'x' and 'y'. Here, x = r 鈭� cos(胃) = 0 鈭� cos(-蟺) = 0. Similarly, y = r 鈭� sin(胃) = 0 鈭� sin(-蟺) = 0.
03

Result

The point in rectangular coordinates, according to the conversion, is (0,0).

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Most popular questions from this chapter

In Exercises 29-32, use a graphing utility to graph the rotated conic. $$ r=\frac{2}{1-\cos (\theta-\pi / 4)} $$

\(r^{2}=\frac{1}{\theta}\)

\(r=4+3 \cos \theta\)

Foci: \((3,2),(3,-4)\); major axis of length 8

Graphical Reasoning Use a graphing utility to graph the polar equation \(r=6[1+\cos (\theta-\phi)]\) for (a) \(\phi=0\), (b) \(\phi=\pi / 4\), and (c) \(\phi=\pi / 2\). Use the graphs to describe the effect of the angle \(\phi\). Write the equation as a function of \(\sin \theta\) for part (c).
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