Answer
The point is $(0,1)$
$r = 1$
$\sin{90^{\circ}} = 1$
$\cos{90}^{\circ} = 0$
$\tan{90}^{\circ}$ = undefined
Work Step by Step
The terminal side of $90^{\circ}$ in standard position is represented by the blue line in the figure. It lies on the positive $y$ axis.
The coordinates of points on the terminal side of $90^{\circ}$ can be given by $(0,a)$, where $a$ is a positive number.
Choosing $a=1$ arbitrarily, the point is $(0,1)$.
To find the distance from the origin to $(0,1)$, we use the distance formula
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(0-0)^2+(1-0)^2}=1$$
$$\therefore r = \boxed{1}$$
$\sin{90^{\circ}} = \dfrac{y}{r} = \dfrac{1}{1} = \boxed{1}$
$\cos{90}^{\circ} = \dfrac{x}{r} = \dfrac{0}{1} = \boxed{0} $
$\tan{90}^{\circ} = \dfrac{y}{x} = \dfrac{1}{0 } = \fbox{undefined
}$
