Question

Question #01799

Answer 1

Polar coordinate is `(r,theta)or (1,(5pi)/3)`

Explanation:

Cartesian coordinate of point A is `x(1/2) ,y(-sqrt3/2)`

Polar coordinate is `(r; theta)`, a distance r from a fixed

point O that is called the pole (or origin) and an angle `theta`

from a fixed direction. A is in `4`th quadrant.

`r= sqrt(x^2+y^2)= sqrt((1/2)^2+(-sqrt3/2)^2) = 1`

`tan alpha =y/x= (sqrt3/2)/(1/2) = sqrt3`

`:. alpha=tan^-1(sqrt3) =pi/3`. Since `theta` is in `4`th

quadrant. `:. theta= 2pi-pi/3=(5pi)/3`

Polar coordinate is `(r,theta)or (1,(5pi)/3)` [Ans]