What is the polar form of ( 5 , 14 ) ?

Question

What is the polar form of             (      5      ,      14      )       ?

pressacvt · Accepted Answer

Step 1Using the formulae that link Cartesian to Polar coordinates.      •          r      2        =          x      2        +          y      2            •    θ    =                  tan                  -          1                            (                  y          x                )            The point (5 , 14 ) is in the 1st quadrant and care must be taken.to ensure that       θ                                        is in the 1st quadrant                    (here   x  =  5 and   y  =  14)            r      2        =          5      2        +          14      2        =    25    +    196    =    221    ⇒    r    =          221      and       θ    =                  tan                  -          1                            (                  14          5                )              =    1.23                                        radians                               and       θ                                        is in the 1st quadrant                    Polar coordinates are therefore             221        ,    1.23    )

Kapalci · Accepted Answer

Step 1Rectangular form             (      x      ,      y      )       can be converted into polar form             (      r      ,      θ      )       as follows :      r    =                            x          2                +                  y          2                                  and              θ    =                  tan                  -          1                            (                  y          x                )            So in this particular case we get      r    =                            5          2                +                  14          2                      =          221            θ    =                  tan                  -          1                            (                  14          5                )              =    70    ,          3      ∘

What is the polar form of <mstyle displaystyle="true"> ( 5 , 1

Answered question

Answer & Explanation

New Questions in Integral Calculus