A line passes through the origin and has slope Squareroot 3

A line passes through the origin and has slope - Squareroot 3. Write the equation of this line in polar form. r = - Squareroot 3 theta =- Squareroot 3 r = - Squareroot 3theta None of the above.

Solution

equation of line passing through (0,0) with slope -3 is

y-0=-3(x-0)

y=-3x

in polar coordinates

x=rcos, y=rsin

rsin=-3rcos

sin_/cos=-3

tan=-3

=tan^-1(-3)

=-tan^-1(3)

=-(_/3)

=(2_/3) is the equation of line in polar form