Chapter 9: Q. 70 (page 584)

In Problems 67–70, the polar equation for each graph is either $r = a + b \cos θ$ or $r = a + b \sin θ, a > 0$ . Select the correct equation and find the values of $a$ and $b$ .

Short Answer

Expert verified

The correct equation for the graph is $r = 1 + 4 \sin θ$

And the value of a is $1$ and bis $4$

Step by step solution

Step 1. Given

The graph:

The polar equations:

$r = a + b \cos θ r = a + b \sin θ$

Step 2. Test for r=a+b cos θ

Substitute the point $(1, 0)$ from the graph in the equation,

$r = a + b \cos θ 1 = a + b \cos (0) 1 = a + b$

Substitute the point $(5, \frac{π}{2})$ from the graph in the equation,

$5 = a + b \cos (\frac{π}{2}) 5 = a$

Step 3. Find b

Substitute $a = 5$ in the equation,

$5 + b = 1 b = - 4$

Since $b > 0$ , it is not a correct equation, so test the other equation.

Step 4. Test the equation r=a+b sin θ

Substitute $(1, 0)$ in the equation,

$1 = a + b \sin (0) a = 1$

Substitute $(5, \frac{π}{2})$ in the equation,

$5 = 1 + b \sin (\frac{π}{2}) 5 - 1 = b b = 4$

Step 5. Find the equation

Substitute $a = 1; b = 4$ in the suitable equation,

$r = 1 + 4 \sin θ$

The polar equation of the given graph is $r = 1 + 4 \sin θ$

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In Problems 67–70, the polar equation for each graph is either $r = a + b \cos θ$ or $r = a + b \sin θ, a > 0$ . Select the correct equation and find the values of $a$ and $b$ .

Short Answer

Step by step solution

Step 1. Given

Step 2. Test for r=a+b cos θ

Step 3. Find b

Step 4. Test the equation r=a+b sin θ

Step 5. Find the equation

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In Problems 67–70, the polar equation for each graph is either r=a+bcosθor r=a+bsinθ,a>0. Select the correct equation and find the values of aand b.

Short Answer

Step by step solution

Step 1. Given

Step 2. Test for r=a+b cos θ

Step 3. Find b

Step 4. Test the equation r=a+b sin θ

Step 5. Find the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Geometry

Decision Maths

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 67–70, the polar equation for each graph is either $r = a + b \cos θ$ or $r = a + b \sin θ, a > 0$ . Select the correct equation and find the values of $a$ and $b$ .