Answer: The correct options are (b) and (d).
Explanation:
It the polar form [tex]r^2=x^2+y^2[/tex], where
[tex]x=r\cos \theta,y=r\sin \theta[/tex]
The polar coordinate are in the form of [tex](r,\theta)[/tex].
From the given figure it is noticed that the value of r is 4 and [tex]\theta=\frac{\pi}{2}[/tex] or [tex]90^{\circ}[/tex] .
So the point is defined as [tex](4,90^{\circ})[/tex] and option b is correct.
The value,
[tex](r\cos \theta, r\sin \theta)=(0,4)[/tex]
Check the each option if we get the same value then that option is correct.
For option a.
[tex](r\cos \theta, r\sin \theta)=(-4\cos 90^{\circ} , -4\sin 90^{\circ})=(0,-4)[/tex]
Therefore option (a) is incorrect.
For option c.
[tex](r\cos \theta, r\sin \theta)=(4\cos (-90)^{\circ} , 4\sin (-90)^{\circ})=(0,-4)[/tex]
Therefore option (c) is incorrect.
For option d.
[tex](r\cos \theta, r\sin \theta)=(-4\cos (270)^{\circ} , -4\sin (270)^{\circ})\\(-4\cos (360-90)^{\circ} , -4\sin (360-90)^{\circ})=(0,4)[/tex]
Therefore option (d) is correct.
For option (e).
[tex](r\cos \theta, r\sin \theta)=(-4\cos (-270)^{\circ} , -4\sin (-270)^{\circ})\\(-4\cos (270)^{\circ} , 4\sin (270)^{\circ})=(0,-4)[/tex]
Therefore option (e) is incorrect.
