Question

draw the terminal side of an angle in standard position that measures $-360^{circ}$.
hint: first plot a point at the origin, then plot a second point anywhere on the terminal side.

a. name a point on the terminal side of the angle.
b. find the distance from the origin to that point.
$r =$
c. name another angle that is coterminal with the angle you have drawn.

Explanation:

Step1: Analyze the angle - 360°

An angle of - 360° in standard position has its terminal side on the positive x - axis. So, a point on the terminal side can be (1,0).

Step2: Calculate the distance from the origin to the point (1,0)

Use the distance formula \(r=\sqrt{(x - 0)^2+(y - 0)^2}\). For the point \((x = 1,y = 0)\), we have \(r=\sqrt{(1 - 0)^2+(0 - 0)^2}=\sqrt{1+0}=1\).

Step3: Find a coterminal angle

Coterminal angles are of the form \(\theta+360^{\circ}n\), where \(n\in\mathbb{Z}\). For \(\theta=-360^{\circ}\), if \(n = 1\), then \(\theta+360^{\circ}n=-360^{\circ}+360^{\circ}=0^{\circ}\)

Answer:

a. \((1,0)\)
b. \(r = 1\)
c. \(0^{\circ}\)