find the polar coordinates of the point with rectangular coordinates (1,-3). approx. if 0<theta<360º?

Answer 1

The distance r from the origin to the point (1,-3) is

r = [1^2 + (-3)^2]^(1/2) = (10)^(1/2)

The angle t from the x-axis to the point is given by

y/x = tan(t) = -3 => t = arctan(-3) = 288.435 degrees.

Answer 2

The distance from (0,0) to (1,-3) is going to be √(1^2 + (-3)^2) = √10, so that's the value of r.

θ stretches into the fourth quadrant, so it's going to be 3π/2 plus the angle in the third quadrant. Looking at the triangle, you can see that the tangent of this angle is -3/1 = -3. So we could say θ = 3π/2 + tan^-1 (-3).

Answer 3

r=sqrt(1+9)=sqrt10
tan theta =-3 so theta 5.0341 rad =288.439 degrees
sqrt10<288.439 deg.