where do i even start with this one

Question

convert the rectangular coordinate pair (4, -7) to two different sets of polar coordinates, one with a positive r-value and one with a negative r-value.

Answer 1

Find length r from r² = x² + y² =65, r = √65 ≅ 8.062. Divide x and y by this number to get cosine and sine values: cos θ = 4/ √65 = 0.4961, sin θ = -7/ √65 = -0.8682. Positive x and negative y puts θ in quadrant IV at -60.26º or -1.052 radians. To get second result, you add 180º or π radians so that the negative radius points in the original direction. Results: (√65, -1.052) and (-√65, 2.090).