Section 10.1 Polar Coordinates

_ Rectangular Coordinates: (3V3, 3) _ _ Rectangular Coordinates: (– 2V2, 2V2)

Polar Coordinates: (3, π/2)

HINT: Use the Pythagorean Theorem to find r and use the Inverse Tangent to find θ. Polar Coordinates:

r 2 = x 2 + y 2 tan θ =

Polar Coordinates:

x 2 + y 2 = 4y x 2 + y 2 – 4y = 0 x 2 + (y 2 – 4y + 4) = (x – 0) 2 + (y – 2) 2 = 4 Circle with center at (0, 2) and radius of 2. HINT: Multiply both sides by r. r 2 = 4 r sin θ Remember: (x – h) 2 + (y – k) 2 = r 2 Center (h, k) Radius r

4xy = 9 4(r cos θ) ( r sin θ) = 9 4r 2 cos θ sin θ = 9 Transform the equation 4xy = 9 from rectangular coordinates to polar coordinates. We use the following formulas: x = r cos θ and y = r sin θ.

A)B) C) D)

A) B) C) D)