Question

Find the rectangular coordinates of the point (-4, pi/3)

Answer 1

Answer:

$\texttt{The rectangular coordinates of the point (-4, pi/3)}=(-2,-2\sqrt{3})$

Step-by-step explanation:

Conversion of parametric form of ( r , θ ) to rectangular coordinate can be done by using the formula ( rcosθ , rsinθ ).

Here we need to convert (-4, pi/3) in to rectangular coordinate form.

Which can be converted to rectangular coordinate form as

         $\left ( -4cos\left ( \frac{\pi}{3} \right),-4sin\left ( \frac{\pi}{3} \right)\right )=\left ( -4\times \left ( \frac{1}{2} \right),-4\times \left ( \frac{\sqrt{3}}{2} \right)\right )=(-2,-2\sqrt{3})$

$\texttt{The rectangular coordinates of the point (-4, pi/3)}=(-2,-2\sqrt{3})$

Answer 2

The point is in Quadrant III; I know that because of the " - " sign.

The angle from the positive x-axis counterclockwise from zero is pi plus pi/3, or 4pi/3.

The x-coordinate of the point is then 4 cos 4pi/3, or -2.

The y-coordinate of the point is 4 sin 4pi/3, or -3.46.

Check:  Is the Pyth. Thm. satisfied here?  Does (-2)^2 + (-3.46)^2 = 4^2?

Yes.  That comes out to 15.97, which is close enough to verify these 2 coordinates are correct.