Question

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

Answer 1

`\bf \begin{array}{rllll} (-5&,&(5\pi )/(3))\\ \uparrow &&\uparrow \\ r&&\theta \end{array}\qquad \begin{cases} x=rcos(\theta )\\ y=rsin(\theta )\\ ----------\\ x=(-5)cos\left( (5\pi )/(3) \right)\\ \qquad -5\cdot (1)/(2)\\ \qquad -(5)/(2)\\ y=(-5)sin\left( (5\pi )/(3) \right)\\ \qquad -5\cdot -(√(3))/(2)\\ \qquad (5√(3))/(2) \end{cases}\implies \left(-(5)/(2)\ ,\ (5√(3))/(2) \right)`