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Chapter 9: Q. 22 (page 583)

Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.
$r = 2 \sin θ$

Short Answer

Expert verified

The graph is

Step by step solution

01

Step 1. Given information

The given polar equation is $r = 2 \sin θ$

02

Step 2. Convert polar equation into rectangular equation and graph it.

$r = 2 \sin θ r^{2} = 2 r \sin θ$

As $y = r \sin θ$ and $r^{2} = x^{2} + y^{2}$

So,

$x^{2} + y^{2} = 2 y x^{2} + y^{2} - 2 y + 1 = 1 x^{2} + {(y - 1)}^{2} = 1$

The graph is

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Most popular questions from this chapter

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(6, 150 °)$

Match the graph with the polar equation.

$r = 2 \sin θ$

In Problems 11–22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.

$3 - 4 i$ .

In Problems 39–54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

$(7.5, 110^{\circ})$

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

${[4 (\cos 40 ° + i \sin 40 °)]}^{3}$

See all solutions

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