Question

How do you find rectangular coordinates for the point with polar coordinates (4, 4pi/3)?

Answer 1

see below

Explanation:

Use the formulas `x=rcos theta, y=rsin theta`

`(r,theta)=(4,(4pi)/3)-->r=4, theta = (4pi)/3`

Hence,

`x=4 cos( (4pi)/3), y=4sin((4pi)/3)`

`x=4*(-1/2)=-2, y=4*(-sqrt3/2)=-2sqrt3`

`:.(x,y)=(-2,-2sqrt3)`