10.3 Polar Coordinates – Math 152, section 4, Spring 2023 Web Assign

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## University

Illinois Institute of Technology

## Course

Calculus Ii (MATH 152)

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Academic year: 2022/2023

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- Homework 1 – Calculus

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Find two other pairs of polar coordinates of the given polar coordinate, one with and one with Then plot the point.

## (a)

## (b)

## r > 0 r < 0.

## ( 5 , ÿ/ 3 )

## (r, ÷) =

## $$5,73π

## (r > 0)

## (r, ÷) =

## $$−5,−5π 3

## (r < 0)

## ( 3 , −5ÿ/ 6 )

## 1. [5/6 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.501.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

### (c)

## (r, ÷) =

## $$3,7π 6

## (r > 0)

## (r, ÷) =

## $$−3,π 6

## (r < 0)

### (−3, ÿ/ 4 )

## (r, ÷) =

## $$3,54π

## (r > 0)

## (r, ÷) =

## $$−3,−74π

## (r < 0)

## The Cartesian coordinates of a point are given.

## (a)

## (i) Find polar coordinates (r, ÷) of the point, where

## (ii) Find polar coordinates (r, ÷) of the point, where

## (b)

## (i) Find polar coordinates (r, ÷) of the point, where

## (ii) Find polar coordinates (r, ÷) of the point, where

## ( 4 , −4)

## r > 0 and 0 ≤ ÷ < 2 ÿ.

## (r, ÷) =

## $$4√2,74π

## r < 0 and 0 ≤ ÷ < 2 ÿ.

## (r, ÷) =

## $$−4√2,34π

## (−1, 3 )

## r > 0 and 0 ≤ ÷ < 2 ÿ.

## (r, ÷) =

## $$2,2π 3

## r < 0 and 0 ≤ ÷ < 2 ÿ.

## (r, ÷) =

## $$−2,5π 3

## 2. [4/4 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.505.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions.

1 < r ≤ 5 , 2 ÿ/ 3 ≤ ÷ ≤ 4 ÿ/ 3

## 3. [1/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.528.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

Sketch the region in the plane consisting of points whose polar coordinates satisfy the given condition.

## 5 ≤ r ≤ 8

## 5. [1/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.533.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

## Find a Cartesian equation for the curve and identify it.

## $$y=

## Find a Cartesian equation for the curve and identify it.

## $$y=x 29

## r = 8 csc(÷)

## hyperbola

## circle

## line

## ellipse

## parabola

## r = 9 tan(÷) sec(÷)

## ellipse

## parabola

## limaçon

## circle

## line

## 6. [2/2 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.521.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

## 7. [2/2 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.508.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

The gure shows the graph of r as a function of ÷ in Cartesian coordinates. Use it to sketch the corresponding polar curve.

## 9. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

The gure shows the graph of r as a function of ÷ in Cartesian coordinates. Use it to sketch the corresponding polar curve.

## 10. [1/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.517.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

Sketch the curve with the given polar equation by rst sketching the graph of r as a function of ÷ in Cartesian coordinates.

## r = cos( 5 ÷)

## 12. [1/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.512.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

Sketch the curve with the given polar equation by rst sketching the graph of r as a function of ÷ in Cartesian coordinates.

## r = 2 cos( 4 ÷)

## 13. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

Sketch the curve with the given polar equation by rst sketching the graph of r as a function of ÷ in Cartesian coordinates.

## r = 5 + 3 sin(÷)

## 15. [1/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.515.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

## r 2 = 6 sin(2÷)

## 16. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

## Sketch the curve with the given polar equation.

Find the slope of the tangent line to the given polar curve at the point specied by the value of ÷.

## $$√ 3

## r = 5 (1 − sin(÷)), ÷ ≥ 0

## r = 4 sin(÷), ÷ = ÿ/

## 18. [1/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.543.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

## 19. [1/1 Points] DETAILS PREVIOUS ANSWERS SCALC9 10.3.519.

### MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

## Video Example

## EXAMPLE 4 What curve is represented by the polar equation

SOLUTION The curve consists of all points with Since r represents the distance from

the point to the pole, the curve represents the (No Response) with center O and radius (No

Response). In general, the equation represents a circle with center O and radius (See the

## gure.)

## Video Example

## EXAMPLE 7 Sketch the curve

SOLUTION Instead of plotting points, we rst sketch the graph of in Cartesian

coordinates in the top gure by shifting the sine curve up one unit. This enables us to read at a glance

the values of r that correspond to increasing values of ÷. For instance, we see that as ÷ increases from

0 to ÿ/2, r (the distance from O) increases from (No Response) to (No Response) , so we sketch the

corresponding part of the polar curve in gure (a). As ÷ increases from ÿ/2 to ÿ, the top gure shows

that r decreases from (No Response) to (No Response) , so we sketch the next part of the curve as

in gure (b). As ÷ increases from ÿ to 3 ÿ/2, r decreases from (No Response) to (No Response) as

shown in part (c). Finally, as ÷ increases from 3 ÿ/2 to 2 ÿ, r increases from (No Response) to (No

Response) as shown in part (d). If we let ÷ increase beyond 2 ÿ or decrease beyond 0, we would

simply retrace our path. Putting together the parts of the curve from gures (a)-(d), we sketch the

complete curve in part (e). It is called a cardioid because it’s shaped like a heart.

## r = 6?

## (r, ÷) r = 6.

## r = 6

## r = a |a|.

## r = 1 + sin(÷).

## r = 1 + sin(÷)

20. [–/0 Points] DETAILS SCALC9 10.3.AE. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

21. [–/0 Points] DETAILS SCALC9 10.3.AE. MY NOTES ASK YOUR TEACHER

10.3 Polar Coordinates – Math 152, section 4, Spring 2023 Web Assign

University: Illinois Institute of Technology

Course: Calculus Ii (MATH 152)

176 Documents

Students shared 176 documents in this course

Find two other pairs of polar coordinates of the given polar coordinate, one with and one with Then plot the point.

(a)

(b)

r

> 0

r

< 0.

(5,

ÿ

/3)

(

r

,

÷

)=

$$5,73

π

(

r

> 0)

(

r

,

÷

)=

$$−5,−5

π

3

(

r

< 0)

(3, −5

ÿ

/6)

1.

[5.25/6 Points] SCALC9 10.3.501.XP.

DETAILS

PREVIOUS ANSWERS

MY NOTES

ASK YOUR TEACHER

PRACTICE ANOTHER