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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 72 (page 568)

The letters x and y represent rectangular coordinates. Write each equation using polar coordinates $(r, 胃)$ .
$4 x^{2} y = 1$

Short Answer

Expert verified

The equation is written using polar coordinates as $4 r^{3} \cos^{2} 胃 \sin 胃 = 1$ .

Step by step solution

01

Step 1. Concept used

If P is a point with polar coordinates $(r, 胃)$ , the rectangular coordinates $(x, y)$ of P are given by

$x = r \cos 胃 y = r \sin 胃$

02

Step 2. Convert into polar coordinates

In the given equation $4 x^{2} y = 1$ , we substitute $r \cos 胃$ for $x$ and $r \sin 胃$ for $y$ we get

$\begin{array}{rcl} 4 x^{2} y & = & 1 \\ 4 {(r \cos 胃)}^{2} r \sin 胃 & = & 1 \\ 4 r^{2} \cos^{2} 胃路 r \sin 胃 & = & 1 \\ 4 r^{3} \cos^{2} 胃 \sin 胃 & = & 1 \end{array}$

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Most popular questions from this chapter

Identify and graph each polar equation. Verify your graph using a graphing utility.

$r = 4 + 2 \sin 胃$

find the unit vector in the same direction as $v$

$v = - 5 i + 12 j$

find the unit vector in the same direction as $v$ $v = 3 i - 4 j$

In Problems 13鈥�28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

$r = 4$

Write the expression in the standard form $a + i b$ .

${[3 (\cos 80 掳 + i \sin 80 掳)]}^{3}$

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