# What is the Cartesian form of (49,(3pi)/4)?

Jul 2, 2017

$\left(- \frac{49}{\sqrt{2}} , \frac{49}{\sqrt{2}}\right)$

#### Explanation:

We're asked to find the rectangular (Cartesian) coordinate of a given polar coordinate.

This can be done using the formulas

$x = r \cos \theta$

$y = r \sin \theta$

Therefore,

x = 49cos((3pi)/4) = color(red)(-49/(sqrt(2))

y = 49cos((3pi)/4) = color(blue)(49/(sqrt(2))

which are the exact values.

The equivalent Cartesian coordinate is thus

$\left(\textcolor{red}{- \frac{49}{\sqrt{2}}} , \textcolor{b l u e}{\frac{49}{\sqrt{2}}}\right)$