Calculus

Polar Equations

Converting Polar Coordinates to Cartesian

         

The point (12,3π4) \left(12, \frac{3\pi}{4} \right) in polar coordinates can be expressed as (a,b)(a, b) in Cartesian coordinates, where aa and bb are real numbers. What is the value of ab?-ab?

Suppose that (a,π6)(a, \frac{\pi}{6}) in polar coordinates represents the same point as (b,7)(b, 7) in Cartesian coordinates. What is the value of a2+b2a^2+b^2?

P=(24,π3)P=(24, \frac{\pi}{3}) in polar coordinates can be expressed as P=(a,b)P=(a, b) in Cartesian coordinates. What is the value of a+b2a+b^2?

If point PP is given in polar coordinates as P=(10,3π4),P=\left(-10, \frac{3\pi}{4}\right), what are the Cartesian coordinates of P?P?

In polar coordinates, the graph of r=46sin(θ)r = 46 \sin(\theta) is a circle. What is the radius of this circle?

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