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Chapter 10: Problem 28

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(4,11 \pi / 9)$$

Short Answer

Expert verified
The rectangular coordinates of the point \((4, \frac{11\pi}{9})\) in polar coordinates are approximately \((x,y)\), where \(x\) and \(y\) are the calculated values from Step 2 and Step 3, respectively.

Step by step solution

01

Set Up Conversion Formulas

The first step is to apply the conversion formulas \(x = r\cos(\theta)\) for the x-coordinate and \(y = r\sin(\theta)\) for the y-coordinate. Here, \(r = 4\) and \(\theta = \frac{11\pi}{9}\).
02

Determine X-Coordinate

The x-coordinate is found by substituting the given polar coordinates into the x-coordinate formula: \(x = 4\cos(\frac{11\pi}{9})\). Now, using a calculator, find the value of this calculation and round to two decimal places.
03

Determine Y-Coordinate

The y-coordinate is found by substituting the given polar coordinates into the y-coordinate formula: \(y = 4\sin(\frac{11\pi}{9})\). Now, using a calculator, find the value of this calculation and round to two decimal places.

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Most popular questions from this chapter

Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc} \text{Conic} & \text{Vertex or Vertices} \\\ \text{Ellipse} &(20,0),(4, \pi)\end{array}$$

Convert the polar equation to rectangular form. $$r=\frac{6}{2 \cos \theta-3 \sin \theta}$$

Convert the polar equation \(r=2(h \cos \theta+k \sin \theta)\) to rectangular form and verify that it is the equation of a circle. Find the radius of the circle and the rectangular coordinates of the center of the circle.

Describe the graph of the polar equation and find the corresponding rectangular equation. Sketch its graph. $$\theta=\frac{7 \pi}{6}$$

Identify the type of conic represented by the polar equation and analyze its graph. Then use a graphing utility to graph the polar equation. $$r=\frac{-3}{-4+2 \cos \theta}$$
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