Answer
The point is $(1,0)$
$r=1$
$\sin({0^{\circ}}) =0$
$\cos({0}^{\circ}) =1$
$\tan({0}^{\circ}) =0$
Work Step by Step
The terminal side of $0^{\circ}$ in standard position is represented by the blue line in the figure. It lies on the positive $x$ axix.
The coordinates of points on the terminal side of $0^{\circ}$ 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
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(1-0)^2+(0-0)^2}=1$$
$$\therefore r = \boxed{1}$$
$\sin({0^{\circ}}) = \dfrac{y}{r} = \dfrac{0}{1} = \boxed{0}$
$\cos({0}^{\circ}) = \dfrac{x}{r} = \dfrac{1}{1} = \boxed{1} $
$\tan({0}^{\circ}) = \dfrac{y}{x} = \dfrac{0}{1 } = \boxed{0}$
