The document discusses converting between polar and rectangular coordinates. Polar coordinates (r, θ) can be converted to rectangular (x, y) using x = r cosθ and y = r sinθ. Rectangular coordinates (x, y) can be converted to polar using r = √(x^2 + y^2) and θ = arctan(y/x), adding 180° to θ when x is negative. It provides examples of converting between polar and rectangular coordinate forms.

1. Precalculus
9-3 Polar and Rectangular Coordinates
The ____________________ coordinates (x, y) of a point (r, θ) can be found using:
EX1: Find the rectangular coordinates for
æ 5p ö
(a) ç −2,-
è ÷ (b) ( 3, 270° )
6 ø
Converting rectangular coordinates (x, y) into polar (r, θ) uses the __________________
________________ and the arctan function.
• The arctan function only works when ____________ (otherwise undefined).
• Therefore, add __________ to θ when x < 0 (to complete the circle … of life).
Conversion formulas:
EX2: Find the polar coordinates of (-8, -12).

2. EX3: Write the polar equation r = 6 χοσθ in rectangular form.
2
EX4: Write the rectangular equation ( x − 3) + ψ = 9 in polar form.
2
HW p. 572 (16 – 22, 28 – 34, 42 even)