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Chapter 9: Q. 6 (page 774)

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

Short Answer

Expert verified

The value of $y = r \sin θ$

Step by step solution

Step 1. Given information

The vertical distance of the point from x-axis is $y$ .

Step 2. Convert y into polar form:

Draw a diagram of a circle of radius $r$ and let a point P(x,y) on the circle:

Apply trigonometric formula of sine in the right angle triangle,

$\sin θ = \frac{y}{r} y = r \sin θ$

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Most popular questions from this chapter

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.

$foci (\pm α, 0), major axis 4 α$

Find a definite integral expression that represents the area of the given region in polar plane and then find the exact value of the expression

The region inside both of the cardioids $r = 3 + 3 \sin θ a n d r = 1 + \sin θ$

In Exercises 60 and 61 we ask you to prove Theorem 9.23 for ellipses and hyperbolas

Consider the ellipse with equation $\frac{x^{2}}{A^{2}} + \frac{y^{2}}{B^{2}} = 1$ where $A > B$ . Let $F$ be the focus with coordinates $(\sqrt{A^{2} - B^{2}}, 0)$ . Let $e = \frac{\sqrt{A^{2} - B^{2}}}{A}$ and l be the vertical line with equation $x = \frac{A}{e}$ . Show that for any point P on the ellipse, $\frac{F P}{D P} = e_{'}$ , where $D$ is the point on $l$ closest to $P$ .

Use polar coordinates to graph the conics in Exercises 44–51.

$r = \frac{2}{4 + \cos θ}$

Complete the square to describe the conics in Exercises 18–21 .

$y^{2} - 8 y - 4 x^{2} - 8 x - 13 = 0$

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert y into polar form:

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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.
$y = . . . . . . . .$