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Section 10.1 Polar Coordinates

Section 10.1 Polar Coordinates

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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: )4

,22(

r2 = x2 + y2

tan θ = x

y

Polar Coordinates: )3

4,2(

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.

A) B)

C) D)

A)

B)

C)

D)