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I have found two solutions to my problem in polar coordinates, but have to submit them to Cartesian coordinate form. How do I convert them?

Point \(A = (2,\frac{\pi}{3})\)

Point \(B = (4,\frac{11\pi}{6})\)

 Feb 20, 2024
 #1
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(r, theta) in polar form, where theta indicates the direction and r, the length. Think of (2, pi/3) as a triangle with diagonal two and angle pi/3 = 60 degrees.

Thus, the base of the triangle, is 2/2 = 1, and then the height would be sqrt(3), so Point A has coordinates (1, sqrt(3)).

Point B likewise, in the fourth quadrant, would have the included angle be 30 degrees with a diagonal of 4. Thus, its coordinates would be (2sqrt(3), -2).

 Feb 20, 2024
 #2
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Thank you! It makes more sense now!

helloworldhello  Feb 22, 2024

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