Answer:
(a) ∴(x,y)= (-2,0)
(b) ∴(x,y)= (-2,[tex]-2\sqrt3[/tex])
(c) ∴(x,y)=[tex](2\sqrt2,-2\sqrt 2)[/tex]
Step-by-step explanation:
To convert from polar coordinate to Cartesian Coordinate(x,y)
(a)
Here r = 2 and θ = π
x= 2 cos π = -2
y= 2 sin π = 0
∴(x,y)= (-2,0)
(b)
Here r = 4 and [tex]\theta=-\frac{2\pi}{3}[/tex]
x= 4 cos [tex](-\frac{2\pi}{3})[/tex] [tex]=4\times (-\frac12)[/tex] = - 2
y= 4 sin [tex](-\frac{2\pi}{3})[/tex] [tex]=4\times (-\frac{\sqrt3}{2})[/tex] =[tex]=-2\sqrt3[/tex]
∴(x,y)= (-2,[tex]-2\sqrt3[/tex])
(c)
Here r= -4 and [tex]\theta= \frac{3\pi}{4}[/tex]
[tex]x=-4 cos (\frac{3\pi}{4})=-4 \times (-\frac1{\sqrt2)}=2\sqrt2[/tex]
[tex]y=-4 sin(\frac{3\pi}{4})=-4\times \frac{1}{\sqrt2} =-2\sqrt 2[/tex]
∴(x,y)=[tex](2\sqrt2,-2\sqrt 2)[/tex]
