Answer
The point is $(-1,0)$
$r=1$
$\sin{180^{\circ}} =0$
$\cos{180}^{\circ} =-1$
$\tan{180}^{\circ} = 0$
Work Step by Step
The terminal side of $180^{\circ}$ in standard position is represented by the blue line in the figure. It lies on the negative $x$ axis.
The coordinates of points on the terminal side of $180^{\circ}$ can be given by $(-a,0)$, where $a$ is a positive number.
Choosing $a=1$ arbitrarily, the point is $(-1,0)$.
To find the distance from the origin to $(-1,0)$, we use the distance formula
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(-1-0)^2+(0-0)^2}=1$$
$$\therefore r = \boxed{1}$$
$\sin{180^{\circ}} = \dfrac{y}{r} = \dfrac{0}{1} = \boxed{0}$
$\cos{180}^{\circ} = \dfrac{x}{r} = \dfrac{-1}{1} = \boxed{-1} $
$\tan{180}^{\circ} = \dfrac{y}{x} = \dfrac{0}{-1 } = \boxed{0}$
