The Cartesian coordinates of a point are given. a) (2,−2) b) (−1,3) Find the polar coordinates (r,θ) of the point, where r is greater than 0 and 0 is less than or equal to θ, which is less than 2π Find the polar coordinates (r,θ) of the point, where r is less than 0 and 0 is less than or equal to θ, which is less than 2π

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The Cartesian coordinates of a point are given.  a) (2,−2)  b) (−1,3)  Find the polar coordinates (r,θ) of the point, where r is greater than 0 and 0 is less than or equal to θ, which is less than 2π  Find the polar coordinates (r,θ) of the point, where r is less than 0 and 0 is less than or equal to θ, which is less than 2π

Mitchel Aguirre · Accepted Answer

Consider the Cartesian coordinates be (x,y).  The polar coordinates (r,θ) is defined as,  r2=x2+y2  x=rcos⁡θ  y=rsin⁡θ  This implies that, tan⁡θ=yx  a) The Cartesian coordinates be (2,−2).  Calculate r and θ as follows:  r2=22+(−2)2  =8  r=±22  tan⁡θ=yx  =−22  =−1  Thus, the angle θ is 3π4,7π4 as the angle 0≤θ2π  The polar coordinates of (2,-2) are,  (22,7π4), where r&amp;gt;0  (−22,3π4), where r&amp;lt;0  b) The Cartesian coordinates be (−1,3).  Calculate r and θ as follows:  r2=(−1)2+(3)2  =4  r=±2  tan⁡θ=yx  =3−1  =−3  Thus, the angle θ is 2π3,5π3 as the angle 0≤θ≤2π  The polar coordinates of (−1,3) are,  (2,2π3), where r&amp;gt;0  (−2,5π3), where r&amp;lt;0

The Cartesian coordinates of a point are given. a) (2,-2) b) (-1,\sqrt{3}) Find the polar coordinates (r,\theta) of the point, where r is greater than

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