Question

What is the rectangular form of the polar equation?

Answer 1

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

tanθ = $\frac{y}{x}$

Given : Polar equation as 'θ' = $-\frac{5\pi }{6}$

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

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

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

$\text{tan}\frac{\pi }{6}$ = $\frac{y}{x}$

$\frac{y}{x}=\frac{\sqrt{3}}{3}$

y = $\frac{\sqrt{3} }{3}x$

Therefore, y = $\frac{\sqrt{3} }{3}x$ will be the rectangular form of the polar equation.

Option (1) will be the correct option.