Hw1 Problem 12

Return to Homework 1, Glossary, Theorems

Problem 12

(a)

(1)

\begin{align} x +_{2\pi} \frac{3\pi}{2} = \frac{3\pi}{4}\enspace in\enspace\mathbb{R}_{2\pi} \end{align}

(b)

(2)

\begin{align} x +_{12} = {2}\enspace in\enspace\mathbb{Z}_{12} \end{align}

Solution

(a)

(3)

\begin{align} x +_\frac{8\pi}{4} \frac{6\pi}{4} = \frac{3\pi}{4}\\ \frac{11\pi}{4} - \frac{6\pi}{4} = \frac{5\pi}{4}\\ x = \frac{5\pi}{4} \end{align}

(b)

(4)

\begin{align} x +_{12} 0 = 2\\ x + 0 = 2\\ x = 2 \end{align}