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Phantasy [73]
2 years ago
10

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

Mathematics
1 answer:
andreev551 [17]2 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

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Answer:

Step-by-step explanation:

First, you want to do inverse operations like I said on the last equation

Just divide  -4 with 64

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Now what is greater than or equal to  -16?

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5 0
2 years ago
16.089 round to nearest 10
zepelin [54]
20 because 16 is greater than 15 and we round the number up.
8 0
3 years ago
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Scorpion4ik [409]

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Step-by-step explanation:

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5 0
2 years ago
Divide (-3х + 4 + 18х^2 )by (5 + 6x)
Leokris [45]

Answer:

The division will be represented as:

\frac{18x^{2}-3x+4}{6x+5}=(3x-3)+\frac{19}{6x+5}

Step-by-step explanation:

1) Let's find a number with a variable that multiplied by 6x gives as 18x². It will be 3x, because (6x+5)3x=18x²+15x.

Now, let's subtstract:

(18x^{2}-3x+4)-(18x^{2}+15x)=-18x+4

2) Let's find a number with a variable that multiplied by 6x gives as -18x. It will be -3, because (6x+5)(-3)=-18x-15.

Now, let's subtstract:

(-18x+4)-(-18x-15)=19  

Therefore, the division will be represented as:

\frac{18x^{2}-3x+4}{6x+5}=(3x-3)+\frac{19}{6x+5}

I hope it helps you!    

5 0
3 years ago
− +  +   7 3 4 18 2 5
zimovet [89]

Answer:

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3 0
2 years ago
Read 2 more answers
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