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Chapter 8: Problem 8

Use the angle feature of a graphing utility to find the rectangular coordinates for the point given in polar coordinates. Plot the point. $$ (8.25,1.3) $$

Short Answer

Expert verified
The polar coordinates (8.25,1.3) convert to the rectangular coordinates approximately (2.2555, 7.8473).

Step by step solution

01

Identify the Polar Coordinates

Recognize that the provided values are polar coordinates are denoted as \( (r, \Theta) \), where \( r \) is the radial distance from the origin and \( \Theta \) is the angle from the positive x-axis. Our given coordinates are \( (8.25, 1.3) \).
02

Convert into Rectangular Coordinates

Convert the polar coordinates to rectangular coordinates using the formulas \( x = r*cos(\Theta) \) and \( y = r*sin(\Theta) \). Applying these formulas gives \( x = 8.25*cos(1.3) \approx 2.2555 \) and \( y = 8.25*sin(1.3) \approx 7.8473 \). Thus, the rectangular coordinates are approximately (2.2555, 7.8473).
03

Plot the point

Plot the point on a graph with the origin at (0,0), the x-coordinate as the horizontal distance from the origin, and the y-coordinate as the vertical distance. Our point is in the first quadrant, as both x and y are positive.

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Most popular questions from this chapter

In Exercises \(17-20,\) use a graphing utility to graph the polar equation. Identify the graph. \(r=\frac{2}{2+3 \sin \theta}\)

Use a graphing utility to graph the polar equation over the given interval. Use the integration capabilities of the graphing utility to approximate the length of the curve accurate to two decimal places. $$ r=2 \sin (2 \cos \theta), \quad 0 \leq \theta \leq \pi $$

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$ x=\tan ^{2} \theta, \quad y=\sec ^{2} \theta $$

In Exercises \(27-38,\) find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) \(\frac{\text { Conic }}{\text { Hyperbola }} \quad \frac{\text { Eccentricity }}{e=\frac{3}{2}} \quad \frac{\text { Directrix }}{x=-1}\)

In Exercises \(7-16,\) find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. \(r=\frac{-6}{3+7 \sin \theta}\)
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