Answer
a. $(3,3)$
b. $3\sqrt{2}$
c. $405^{\circ}$
Work Step by Step
a.
The terminal side of $45^{\circ}$ in standard position is in the 1st quadrant. It lies along the line $y=x$. The terminal side is represented by the blue line in the figure.
The coordinates of points on the terminal side of $45^{\circ}$ can be given by $(a,a)$, where $a$ is a positive number.
Choosing $a=3$ arbitrarily, the point is $(3,3)$.
b.
To find the distance from the origin to $(3,3)$, we use the distance formula
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(3-0)^2+(3-0)^2}=\sqrt{18}=\sqrt{9\times2}$$
$$\therefore r = 3\sqrt{2}$$
c.
To find an angle that is coterminal with $45^{\circ}$, we traverse a full revolution in the positive or negative direction.
Positive coterminal angle = $45^{\circ}+360^{\circ}= 405^{\circ}$
