Question

a represent the list of angle measures (in radians) for angles co - terminal with an angle measuring - 3π/6 radians. (use the variable n to denote the integer multiple of 2π in your expression)
b represent the list of angle measures (in radians) for angles co - terminal with an angle measuring 2 radians. (use the variable n to denote the integer multiple of 2π in your expression)

Explanation:

Part a

Step1: Recall co - terminal angles formula

Co - terminal angles of an angle \(\theta\) (in radians) are given by \(\theta + 2n\pi\), where \(n\) is an integer. Here, the given angle is \(-\frac{3\pi}{6}=-\frac{\pi}{2}\).

Step2: Write the expression for co - terminal angles

Using the formula for co - terminal angles, the co - terminal angles of \(-\frac{\pi}{2}\) (or \(-\frac{3\pi}{6}\)) are \(-\frac{\pi}{2}+2n\pi\), where \(n\in\mathbb{Z}\) ( \(n\) is an integer). We can also simplify \(-\frac{3\pi}{6}\) to \(-\frac{\pi}{2}\), and the general form of co - terminal angles is \(-\frac{\pi}{2}+2n\pi\) or \(-\frac{3\pi}{6}+2n\pi\).

Step1: Recall co - terminal angles formula

Co - terminal angles of an angle \(\theta\) (in radians) are given by \(\theta+ 2n\pi\), where \(n\) is an integer. Here, the given angle is \(2\) radians.

Step2: Write the expression for co - terminal angles

Using the formula for co - terminal angles, the co - terminal angles of \(2\) radians are \(2 + 2n\pi\), where \(n\in\mathbb{Z}\) ( \(n\) is an integer).

Answer:

\(-\frac{\pi}{2}+2n\pi\) (or \(-\frac{3\pi}{6}+2n\pi\))

Part b