Question

Convert y=9 from rectangular to polar form

Answer 1

`r=9csc(\theta)`

Explanation:

To convert from polar coordinates to rectangular coordinates you must use the following equivalence equations

`x=rcos(\theta)` i

`y=rsin(\theta)` ii

In this case we have the following equation

`y=9` So we use equation ii

`rsin(\theta)=9`

`r=(9)/(sin(\theta))`

Remember that
`csc(\theta)=(1)/(sin(\theta))`

So

`r=9csc(\theta)`

Answer 2

r = 9/sin Ф or r = 9 csc Ф

Explanation:

The polar form is represented as:

x = r cos Ф and

y = r sin Ф

We are given:

y = 9

Putting value in y = r sin Ф

9 = r sin Ф

=> r = 9/sin Ф

1/sin Ф = csc Ф

or, r = 9 csc Ф