Find an equation equivalent to y = x in polar coordinates.

General flow:
1) Transform x and y to polar coordinate
2) Plug it into the orginal equation
3) Do some work to manipulate it!
From step 1, we have x = r cosθ, y = r sinθ
From step 2, we have
y = x
r sinθ = r cosθ
r (sinθ - cosθ) = 0
That means r = 0 or sinθ - cosθ = 0. You only need to play around with sinθ - cosθ = 0
Can you do step 3?

Answer Link

Lanuel Lanuel · Answer 2 · 2022-04-25T20:34:31+02:00

An equation that is equivalent to y = x in polar coordinates is given by sinθ = cosθ.

How to convert rectangular coordinates to polar coordinates.

In geometry, the relationship between the rectangular coordinates (x, y) and polar coordinates (r, θ) is given by these mathematical equations:

x = rcosθ .......equation 1.

y = rsinθ .......equation 2.

Equating the equations, we have:

y = x ⇒ rsinθ = rcosθ

Divding both sides by r, we have:

rsinθ/r = rcosθ/r

sinθ = cosθ.

Read more on polar coordinates here: https://brainly.com/question/2193539