Answer
a. $(0,3)$
b. $3$
c. $-270^{\circ}$
Work Step by Step
a.
The terminal side of $90^{\circ}$ in standard position is on the positive $y$ axis. The terminal side is represented by the blue line in the figure.
The coordinates of points on the terminal side of $90^{\circ}$ can be given by $(0,a)$, where $a$ is a positive number.
Choosing $a=3$ arbitrarily, the point is $(0,3)$.
b.
To find the distance from the origin to $(0,3)$, we use the distance formula
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(0-0)^2+(3-0)^2}=\sqrt{9}=3$$
$$\therefore r = 3$$
c.
To find an angle that is coterminal with $90^{\circ}$, we traverse a full revolution in the positive or negative direction.
Negative coterminal angle = $90^{\circ}-360^{\circ}= -270^{\circ}$
