Determine whether the statement is true or false Give justif

Determine whether the statement is true or false. Give justification to your answers. (a) If theta_1 = theta_2 + 2 pi n, then (r, theta_1) and (r, theta_2) represent the same point in polar coordinates. (b) If | r_1 | = | r_2 |, then (r_1, theta) and (r_2, theta) represent the same point in polar coordinates.

Solution

(a.)Yes. because in polar cordinate for any trigonmetry funtion value is same for ( 2*pie*n +theta) as it is for theta.

(b.) Yes.

since mod(r1)=mod(r2) so both represent the same points.