Question

The cartesian coordinates of the points, whose polar coordinates are $(5,-\frac{\pi }{4})$, are

• A. $(\frac{5}{\sqrt{2}},\frac{5}{\sqrt{2}})$
• B. $(\frac{5}{\sqrt{2}},\frac{-5}{\sqrt{2}})$
• C. $(\frac{-5}{\sqrt{2}},\frac{5}{\sqrt{2}})$
• D. $(\frac{-5}{\sqrt{2}},\frac{-5}{\sqrt{2}})$

Answer 1

The correct option is B $(\frac{5}{\sqrt{2}},\frac{-5}{\sqrt{2}})$

Given $(r,\theta )=(5,-\frac{\pi }{4})$
We have,
$x=r\cos \theta$, $y=r\sin \theta$
$x=5\cos (-\frac{\pi }{4}),y=5\sin (-\frac{\pi }{4})$
$x=\frac{5}{\sqrt{2}},y=-\frac{5}{\sqrt{2}}$
So, the cartesian form is $(\frac{5}{\sqrt{2}},-\frac{5}{\sqrt{2}})$