Question

The cartesian co-ordinates of the point whose polar co-ordinates are as $(5,\pi -{\tan }^{-1}\left(\frac{4}{3}\right))$, are

• A. $(-3,-4)$
• B. $(-3,4)$
• C. $(3,-4)$
• D. $(3,4)$

Answer 1

The correct option is B $(-3,4)$

$(5,\pi -{\tan }^{-1}\left(\frac{4}{3}\right))$
$r=5,\theta =\pi -{\tan }^{-1}\left(\frac{4}{3}\right)$
Since, $\theta =\pi -{\tan }^{-1}\left(\frac{4}{3}\right)$,
and since the point lies in second quadrant,
So, $\cos \theta =-\frac{3}{5},\sin \theta =\frac{4}{5}$
We have $x=r\cos \theta ,y=r\sin \theta$
$x=-3,y=4$
So, the point is $(-3,4).$