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Chapter 9: Q. 3 (page 774)

Fill in the blanks to convert between rectangular coordinates and polar coordinates.
$r = . . . . . . . . . . . . . . .$

Short Answer

Expert verified

The value of $r = \sqrt{x^{2} + y^{2}}$

Step by step solution

Step 1. Given information

$r$ is the distance of the point from the origin.

Step 2. Convert r into rectangular coordinate.

Draw a diagram of a circle of radius $r$ and let a pointlocalid="1652261998898" $P (x, y)$ on the circle

Here in the right angle triangle we can apply Pythagorous theorem:

$r^{2} = x^{2} + y^{2} r = \sqrt{x^{2} + y^{2}}$

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Most popular questions from this chapter

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral

The limacon $r = 2 + \cos θ$

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral

The entire limacon $r = 1 + 2 \sin θ$

Complete example 2 by evaluating the integral expression

$\int_{0}^{\frac{2 π}{3}} {(\frac{1}{2} + \cos θ)}^{2} d θ - \int_{π}^{\frac{4 π}{3}} {(\frac{1}{2} + \cos θ)}^{2} d θ$

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38–43.

$foci (\pm 2, 0), directrices x = \pm 1$

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$r = \frac{α}{1 + \sin θ}$

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Fill in the blanks to convert between rectangular coordinates and polar coordinates.r=...............

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert r into rectangular coordinate.

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Most popular questions from this chapter

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Fill in the blanks to convert between rectangular coordinates and polar coordinates.
$r = . . . . . . . . . . . . . . .$