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, (5 \pi)/(3))`

We convert to rectangular coordinates using


`(x,y)=(-7 \cos (5 \pi)/(3) , -7 \sin (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 (\pi)/(3), 7 \sin (\pi)/(3))`

Of course 60 degrees is the biggest cliche in trig.



`(x,y) = (-7 (\frac 1 2), 7( (√(3))/(2)) )`


`(x,y) = (-(7)/(2), (7√(3))/(2) )`