Question

What is the rectangular form of the polar equation?

0=-
57
y=x
V3
Oy= 32
y=-3x

Answer 1

Option (1)

Explanation:

From the picture attached,

tanθ =
`(y)/(x)`

Given : Polar equation as 'θ' =
`-(5\pi )/(6)`

Therefore,
`\text{tan}(-(5\pi )/(6) )` =
`(y)/(x)`

`-\text{tan}((5\pi )/(6) )` =
`(y)/(x)` [Since tan(-θ) = -tanθ]

`\text{tan}(\pi -(5\pi )/(6) )` =
`(y)/(x)` [Since -tanθ = tan(π - θ)]

`\text{tan}(\pi )/(6)` =
`(y)/(x)`

`(y)/(x)=(√(3))/(3)`

y =
`(√(3) )/(3)x`

Therefore, y =
`(√(3) )/(3)x` will be the rectangular form of the polar equation.

Option (1) will be the correct option.