How do you convert #y = -3# to polar form?

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Answer 1 · 2018-05-19T11:04:40

#rsintheta=-3#

Imagine we have a point #P# with Rectangular (also called Cartesian) coordinates #(x,y)# and Polar coordinates #(r,theta)#.

The following diagram will help us visualise the situation better:

We can see that a right triangle is formed with sides #x#, #y# and #r#, as well as an angle #theta#.

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

By Pythagora's theorem, we get the result

#r^color(red)2=x^color(Red)2+y^color(red)2#

The only properties we can say about #theta# are its trigonometric functions:

#sintheta=y"/"r=>y=rsintheta#
#costheta=x"/"r=>x=rcostheta#

So we have the following relations:

#{(r^2=x^2+y^2),(y=rsintheta),(x=rcostheta):}#

Now, we can see that saying #y=-3# in the Rectangular system is equivalent to say

#color(blue)(rsintheta=-3)#

Answer 2 · 2018-05-19T11:08:10

#r=-3/sintheta#

#"to convert from "color(blue)"cartesian to polar"#

#•color(white)(x)x=rcostheta" and "y=rsintheta#

#rArrrsintheta=-3rArrr=-3/sintheta#