section 10.1 polar coordinates
TRANSCRIPT
HINT: Use the Pythagorean Theorem to find r and use the Inverse Tangent to find θ.
Polar Coordinates: )4
,22(
x2 + y2 = 4y
x2 + y2 – 4y = 0
x2 + (y2 – 4y + 4) = 0 + 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 = r2 Center (h, k) Radius r
4xy = 9
4(r cos θ) ( r sin θ) = 9
4r2 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.