1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Phantasy [73]
3 years ago
10

Rewrite the Cartesian equation y=-3 as a polar equation.

Mathematics
1 answer:
andreev551 [17]3 years ago
4 0

r

sin

θ

=

−

3

Explanation:

Imagine we have a point  

P

with Rectangular (also called Cartesian) coordinates  

(

x

,

y

)

and Polar coordinates  

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides  

x

,  

y

and  

r

, as well as an angle  

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about  

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying  

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from  

cartesian to polar

∙

x

x

=

r

cos

θ

and  

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

You might be interested in
Rosie spent $25 on a new DVD. What integer represents Rosie’s situation? A 50, B -25, C 0, D 25
Alborosie
I think b or d are answer ...
8 0
3 years ago
What is the midpoint
Tamiku [17]
Midpoint formula:

x, y = (x2+x1/2), (y2+y1/2)

x, y= (3+8/2), (4-4/2)

x, y= (5.5), (0)

Therefor the midpoint is (5.5, 0)

Hope I helped :)
7 0
3 years ago
An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
Vsevolod [243]

Answers:

a = 2

b = 3

=======================================================

Explanation:

Plug in x = 0 and y = 2 to find that

y = a*b^x

2 = a*b^0

2 = a*1

2 = a

a = 2

Then plug in x = 3 and y = 54 to determine the value of b

y = a*b^x

y = 2*b^x

54 = 2*b^3

2b^3 = 54

b^3 = 54/2

b^3 = 27

b = (27)^(1/3)

b = 3

So we have y = a*b^x update to y = 2*3^x

7 0
3 years ago
Which line is parallel to y= = 1/3x + 7?
Monica [59]
The answer is the third choic, or the line with the same slope.
8 0
3 years ago
Read 2 more answers
Please help me with this.. I am DYING.. I hav no idea what Im getting wrong..?
Oliga [24]

Answer:

12 2/12

or 12 1/6 ( simplified fraction)

Step-by-step explanation:

first add the whole numbers together :7+5-4+3=12-1=11 ( same denominator 12)

1/12 +7/12 -5/12 +11/12 = 14/12  ( improper fraction)

= 1 2/12 mixed fraction

11 + 1 2/12=12 2/12 or 12 1/6 ( simplified fraction)

7 0
3 years ago
Read 2 more answers
Other questions:
  • Steps for solving 4x - 12 =20 are shown. explain how step 3 helps sovle the equation.
    14·2 answers
  • 2x + 5y = 0 <br> x - 5y = -15
    11·1 answer
  • Please simplify....picture attached
    14·2 answers
  • - A rectangle has a width of 4.2 m and an area of 37.8 m2. Find the length and the
    6·1 answer
  • Divide: 21 and 4,291,678
    8·2 answers
  • What is the dollar value of p pennies and d dimes?
    13·1 answer
  • Math need exact anwser pls!!!!!!
    15·1 answer
  • (x + 3x3 + 8x2) - (8x – 7x3 + 7x2)
    7·2 answers
  • With her new trainer, Judy now bikes at an average speed of 24.1 MPH. That is 20.5% faster than she averaged with her old traine
    13·2 answers
  • What is the rule for this pattern?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!