Polar coordinates of a point are given. Find therectangular coordinates of the point. ( − 3 , − 135 ∘ )

Question

Polar coordinates of a point are given. Find therectangular coordinates of the point.   (  −  3  ,  −      135          ∘        )

sviudes7w · Accepted Answer

That&#039;s not what I got.... I figured that since we&#039;re working with apoint in quadrant III, then the reference angle is 45 degrees,making it a   1  −  1  −      2   triangle.Since   cos  ⁡  (  45  )  =      x          −      3      , then   x  =  −  3  cos  ⁡  (  45  )  =            −      3              2      By the same means, y equals the same value (since sin 45 and cos 45 are equal)So the point is (            −      3              2        ,            −      3              2      )

Cristofer Graves · Accepted Answer

Given the polar coordinates: (r,   θ) = (-3, -135degrees)Convert degrees to radians: (r,   θ) = (-3, -3  π/4radians)Use the following conversion:  x  =  r  cos  ⁡  θ  x  =  −  3  cos  ⁡  (  −  3  π      /    4  )  x  =            −      3        1    ∗            −              2              2    =            3              2              2    y  =  r  sin  ⁡  θ  y  =  −  3  sin  ⁡  (  −  3  π      /    4  )  y  =            −      3        1    ∗            −              2              2    =            3              2              2  Rectangular Coordinates are   (  x  ,  y  )  ⇒  (            3              2              2    ,            3              2              2    )

Polar coordinates of a point are given. Find therectangular coordinates of the point. (-3,-135^(circ))

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