What is the polar form of (16, -4)?

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Scarlet Reid · Accepted Answer

Step 1The quickest method is to use the formula:            (      x      ,      y      )        =          (                                    x            2                    +                      y            2                              ,              arctan                  (                      y            x                    )                    )      Below is an alternative method.      x    =    r          cos      θ            y    =    r          sin      θ            16    =    r          cos      θ            -    4    =    r          sin      θ      Step 2Squaring both equations:      256    =          r      2                      cos        2                    (        θ        )                  16    =          r      2                      sin        2                    (        θ        )            Adding both equations:      272    =          r      2                      cos        2                    (        θ        )              +          r      2                      sin        2                    (        θ        )                  272    =          r      2              (                        cos          2                          (          θ          )                    +                        sin          2                          (          θ          )                    )            272    =          r      2              (      1      )        ⇒    r    =    ±                  272              =    ±    4                  17            We only need the positive root, negative radii can exist, and a point can be represented by many different polar coordinates, unlike Cartesian coordinates which are unique.      θ    =          arctan              (                  y          x                )              =          arctan              (        -                  4          16                )              =          arctan              (        -                  1          4                )              =    -    0.24498  Polar coordinate:            (      4                        17                    ,      -      0      ,      245      )

What is the polar form of (16, -4)?

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