Flashcard 11 - Upper Level: Mathematics Achievement Flashcard Set for the ISEE

Polar coordinates are in the form (r, θ). If x and y are known, r and θ can be determined using these formulas:

\[r = \sqrt{x^2 + y^2}\] \[tan θ = \frac {y}{x}\]

For example: What are the polar coordinates of point (2, 3)?

Equation: \(r = \sqrt {4 + 9} = \sqrt {13}\)

tan θ = \(\frac {3}{2}\), and evaluating the arctan of both sides to solve for θ: θ = arctan(\(\frac{3}{2}\)) = \(56.31^\circ\)

The polar coordinates of this point are \((\sqrt{13}, 56.31^\circ)\)