draw the terminal side of an angle in standard position that measures $- 2\\pi$ radians.\nhint: first plot a…

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles can be found by adding or subtracting (2\pi n) (where (n) is an integer) to the given angle (\theta). The formula is (\theta + 2\pi n).

Step2: Find a non - negative coterminal angle

Given (\theta=- 2\pi). Let (n = 1). Then (\theta+2\pi n=-2\pi + 2\pi\times1). [ \begin{align*} -2\pi+2\pi\times1&=-2\pi + 2\pi\ &=0\pi \end{align*} ]

Step3: Find a negative coterminal angle

Let (n=-1). Then (\theta + 2\pi n=-2\pi+2\pi\times(-1)). [ \begin{align*} -2\pi+2\pi\times(-1)&=-2\pi-2\pi\ &=-4\pi \end{align*} ]

Answer:

Non - negative coterminal angle: (0\pi). Negative coterminal angle: (-4\pi).