Find all polar coordinates of point P where P 3 3 a 3 3 2n

Find all polar coordinates of point P where P = (3, -/3)

a. (3, -/3 + 2n) or (-3, -/3 + (2n + 1))

b. (3, -/3 + 2n) or (-3, -/3 + 2n)

c. (3, -/3 + 2n) or (3, -/3 + (2n + 1))

d. (3, -/3 + (2n + 1)) or (-3, -/3 + 2n)

Solution

polar coordinate is of the form ( r , theta )

which can be written as

( r , theta + 2npi ) or ( -r , theta + ( 2n + 1) pi )

so , ( 3, -pi/3 ) can be written as

( 3 , -pi/3 + 2npi ) or ( -3 , -pi/3 + ( 2n+ 1) pi )

option a is correct