Question

Find the rectangular coordinates of the point with the polar coordinates ordered pair negative 7 comma 5 pi divided by 3.

Answer 1

Polar coordinates

$(r, \theta) = (-7, \dfrac{5 \pi}{3})$

We convert to rectangular coordinates using

$(x,y)=(-7 \cos \dfrac{5 \pi}{3} , -7 \sin \dfrac{5 \pi}{3})$

We'll negate the angle (and add two pi) which negates the sine but leaves the cosine alone.

$(x,y)=(-7 \cos \dfrac{\pi}{3}, 7 \sin \dfrac{\pi}{3})$

Of course 60 degrees is the biggest cliche in trig.


$(x,y) = (-7 (\dfrac 1 2), 7( \dfrac{\sqrt{3}}{2}) )$

$(x,y) = (-\dfrac{7}{2}, \dfrac{7\sqrt{3}}{2} )$