The Cartesian coordinates of a point are given. (i) Find polar coordinates (r,θ) of the point, where r &gt; 0 and 0≤θ&lt;2π (ii) Find polar coordinates (r,θ) of the point, where r &lt; 0 and 0≤θ&lt;2π . (2, -2)

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The Cartesian coordinates of a point are given. (i) Find polar coordinates (r,θ) of the point, where r &amp;gt; 0 and 0≤θ&amp;lt;2π (ii) Find polar coordinates (r,θ) of the point, where r &amp;lt; 0 and 0≤θ&amp;lt;2π . (2, -2)

Jennifer Hill · Accepted Answer

Step1  |r|=22+(−2)2=4+4=8=22  Singe  r&amp;gt;0,  we can write  r=22  Step2  Recall that:  rcos⁡θ=x  Therefore  22cos⁡θ=2  Divide both sides by  22  cos⁡θ=12 Equation1  Step3  Recall that:  rsin⁡θ=y  Therefore  22sin⁡θ=−2  Divide both sides by  22  sin⁡θ=−12 Equation 2  Step4  Equation 1 and 2 are satisfied by θ=7π4  Polar coordinates of the point are   (22,7π4)

Clara Clark · Accepted Answer

Step1 |r|=22+(−2)2=4+4=8=22 Singe  r&amp;lt;0,  we can write  r=−22 Step2 Recall that: rcos⁡θ=x Therefore 22cos⁡θ=2 Divide both sides by  −22 cos⁡θ=−12 Equation1 Step3 Recall that: rsin⁡θ=y Therefore −22sin⁡θ=−2 Divide both sides by  −22 sin⁡θ=12 Equation 2 Step4 Equation 1 and 2 are satisfied by θ=7π4 Polar coordinates of the point are (22,7π4) Step 5 Equation 1 and 2 are satisfied by θ=3π4 Polar coordinates of the point are (−22,3π4)

The Cartesian coordinates of a point are given. (i) Find polar coordinates (r

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