# To determine: a) Whether the statement, " The point with Cartesian coordinates $( -2,\ 2 )$ has polar coordinates \[\bf \left( 2 \sqrt{2},\ \frac{3

To determine:
a) Whether the statement, " The point with Cartesian coordinates has polar coordinates " is true or false.
b) Whether the statement, " the graphs of intersect exactly once " is true or false.
c) Whether the statement, " the graphs of intersect exactly once ", is true or false.
d) Whether the statement, " the point " is true or false.
e) Whether the statement, " the graphs of are lines " is true or false.

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delilnaT

a)
The polar coordinate $\left[\begin{array}{cc}r& \theta \end{array}\right]$ corresponding to Cartesian coordinate
From the given data,
Substitute and obtain the value of r.

$=±\sqrt{8}$

Similary, calculate the value of $\left[\theta \right]$ as follows.
$\theta ={\mathrm{tan}}^{-1}\left(-\frac{2}{2}\right)$
$={\mathrm{tan}}^{-1}\left(-1\right)$

For
For
For .
For
Hence the given stament is true.
b) Note that the Cartesian coordinates corresponding to polar coordinates