Question

Find all polar coordinates of point P = (2, 14°).

Answer 1

The polar coordinates of point P are :

`\begin{gathered} (2,14^(\circ)+360n)\quad and\quad(-2,14^(\circ)+180(2n+1)) \\ \text{ where n is any integer} \end{gathered}`

EXPLANATION :

Note that :

`\begin{gathered} \text{ The polar coordinate }(r,\theta)\text{ can be written as :} \\ (r,\theta)\rightarrow(r,\theta+360n) \\ or \\ (-r,\theta)\rightarrow(r,\theta+180(2n+1)) \end{gathered}`

For the positive value of r, the polar coordinate can be written as :

`\begin{gathered} P=(2,14^(\circ))=(2,14^(\circ)+360n) \\ \text{ where n is any integer} \end{gathered}`

For the negative value of r, the polar coordinate can be written as :

`\begin{gathered} P=(-2,14^(\circ))=(-2,14^(\circ)+180(2n+1)) \\ \text{ where n is any integer} \end{gathered}`