Question

Find the Cartesian coordinates of the given polar coordinates. Then plot the point. (a) (2, π) (x, y) = WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot ((b) (4, −2π/3) (x, y) = WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (c) (−4, 3π/4) (x, y) = WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot

Answer 1

Answer:

(a) ∴(x,y)= (-2,0)

(b) ∴(x,y)= (-2,$-2\sqrt3$)

(c) ∴(x,y)=$(2\sqrt2,-2\sqrt 2)$

Step-by-step explanation:

To convert from polar coordinate to Cartesian Coordinate(x,y)

• x = r cos θ
• y = r sin θ

(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 $\theta=-\frac{2\pi}{3}$

x= 4 cos $(-\frac{2\pi}{3})$  $=4\times (-\frac12)$ = - 2

y=  4 sin $(-\frac{2\pi}{3})$  $=4\times (-\frac{\sqrt3}{2})$ =$=-2\sqrt3$

∴(x,y)= (-2,$-2\sqrt3$)

(c)

Here r= -4  and $\theta= \frac{3\pi}{4}$

$x=-4 cos (\frac{3\pi}{4})=-4 \times (-\frac1{\sqrt2)}=2\sqrt2$

$y=-4 sin(\frac{3\pi}{4})=-4\times \frac{1}{\sqrt2} =-2\sqrt 2$

∴(x,y)=$(2\sqrt2,-2\sqrt 2)$