Find the corresponding rectangular coordinates for the point.

[Lebombo]

Homework Statement

Find the corresponding rectangular coordinates for the point. (-2, $\frac{5\pi}{3}$)



x = -2cos($\frac{5\pi}{3}$)

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

x = -2* $\frac{-1}{2}$ = 1



y = -2sin($\frac{5\pi}{3}$)

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

y = -2*$\frac{\sqrt{3}}{2}$ = -$\sqrt{3}$


So the coordinate is (1, -$\sqrt{3}$)

This is my conclusion, however, the answer I found online does not agree: (1, -2)


Am I incorrect? If so, what am I not doing correctly?

 

[LCKurtz]

Homework Statement

Find the corresponding rectangular coordinates for the point. (-2, $\frac{5\pi}{3}$)

I assume that is in polar coordinates, with negative radius.

x = -2cos($\frac{5\pi}{3}$)

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

Are you sure those are equal?

x = -2* $\frac{-1}{2}$ = 1
y = -2sin($\frac{5\pi}{3}$)

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

Same problem. Are you sure those are equal?

y = -2*$\frac{\sqrt{3}}{2}$ = -$\sqrt{3}$So the coordinate is (1, -$\sqrt{3}$)

This is my conclusion, however, the answer I found online does not agree: (1, -2)

That online answer is wrong. Fix your signs and you will have it.

 

[Lebombo]

I assume that is in polar coordinates, with negative radius.

Yes, I should have mentioned the type of coordinates.

Fix your signs and you will have it.

x = -2cos($\frac{5\pi}{3}$)

x = 2cos($\frac{2\pi}{3}$)

x = 2* $\frac{-1}{2}$ = -1



y = -2sin($\frac{5\pi}{3}$)

y = 2sin($\frac{2\pi}{3}$)

y = 2*$\frac{\sqrt{3}}{2}$ = $\sqrt{3}$


So the coordinate is (-1, $\sqrt{3}$)

Like this?

 

[Tanya Sharma]

Yes...(-1,√3) is the correct answer .