Question

Find the polar coordinates of the point whose rectangular coordinates are(squareroot(3),1)

Answer 1

Answer:

The polar coordinates are $(2,\frac{\pi}{6})$.

Step-by-step explanation:

The rectangular coordinates of a point are

$(\sqrt{3},1)$

The polar coordinates are defined as $(r,\theta)$.

The rectangular coordinates of a point are in the form of

$(rcos\theta,rsin\theta)$

Where, $\tan \theta=\frac{y}{x}$ and $r^2=x^2+y^2$.

From the given point it is noticed that the value of x is $\sqrt{3}$ and the value of y is 1.

$\tan \theta=\frac{1}{\sqrt{3}}$

$\tan \theta=\tan (\frac{\pi}{6})$

$\theta=\frac{\pi}{6}$

$r^2=(\sqrt{3})^2+(1)^2$

$r^2=4$

$r=2$

The polar coordinates are $(2,\frac{\pi}{6})$.