Notes

Questions
Find 2 coterminal angles (one positive and one negative)
\(\textbf{1)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=100^{\circ}\)
The answer is \(460^{\circ},\,-260^{\circ}\)
\(\,\,\,\,\,100^{\circ}+360^{\circ}=460^{\circ}\)
\(\,\,\,\,\,100^{\circ}-360^{\circ}=-260^{\circ}\)
\(\textbf{2)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=641^{\circ}\)
The answer is \(281^{\circ},\,-79^{\circ}\)
\(\,\,\,\,\,641^{\circ}-360^{\circ}=281^{\circ}\)
\(\,\,\,\,\,281^{\circ}-360^{\circ}=-79^{\circ}\)
\(\textbf{3)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=-281^{\circ}\)
The answer is \(79^{\circ},\,-641^{\circ}\)
\(\,\,\,\,\,-281^{\circ} + 360^{\circ} = 79^{\circ}\)
\(\,\,\,\,\,79^{\circ} – 360^{\circ} = -641^{\circ}\)
\(\textbf{4)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=40^{\circ}\)
The answer is \(400^{\circ},\,-320^{\circ}\)
\(\,\,\,\,\,40^{\circ} + 360^{\circ} = 400^{\circ}\)
\(\,\,\,\,\,40^{\circ} – 360^{\circ} = -320^{\circ}\)
\(\textbf{5)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{\pi}{3}\)
The answer is \(\frac{7\pi}{3},\,-\frac{5\pi}{3}\)
\(\,\,\,\,\,x=\frac{\pi}{3} + 2\pi = \frac{\pi}{3} + \frac{6\pi}{3} = \frac{7\pi}{3}\)
\(\,\,\,\,\,x=\frac{\pi}{3} – 2\pi = \frac{\pi}{3} – \frac{6\pi}{3} = -\frac{5\pi}{3}\)
\(\textbf{6)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{3\pi}{4}\)
The answer is \(\frac{11\pi}{4},\,-\frac{5\pi}{4}\)
\(\,\,\,\,\,x=\frac{3\pi}{4} + 2\pi = \frac{3\pi}{4} + \frac{8\pi}{4} = \frac{11\pi}{4}\)
\(\,\,\,\,\,x=\frac{3\pi}{4} – 2\pi = \frac{3\pi}{4} – \frac{8\pi}{4} = -\frac{5\pi}{4}\)
\(\textbf{7)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{7\pi}{15}\)
The answer is \(\frac{37\pi}{15},\,-\frac{23\pi}{15}\)
\(\,\,\,\,\,x=\frac{7\pi}{15} + 2\pi = \frac{7\pi}{15} + \frac{30\pi}{15} = \frac{37\pi}{15}\)
\(\,\,\,\,\,x=\frac{7\pi}{15} – 2\pi = \frac{7\pi}{15} – \frac{30\pi}{15} = -\frac{23\pi}{15}\)
\(\textbf{8)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{\pi}{7}\)
The answer is \(\frac{15\pi}{7},\,-\frac{13\pi}{7}\)
\(\,\,\,\,\,x=\frac{\pi}{7} + 2\pi = \frac{\pi}{7} + \frac{14\pi}{7} = \frac{15\pi}{7}\)
\(\,\,\,\,\,x=\frac{\pi}{7} – 2\pi = \frac{\pi}{7} – \frac{14\pi}{7} = -\frac{13\pi}{7}\)
\(\textbf{9)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=215^{\circ}\)
The answer is \(575^{\circ},\,-145^{\circ}\)
\(\,\,\,\,\,215^{\circ}+360^{\circ}=575^{\circ}\)
\(\,\,\,\,\,215^{\circ}-360^{\circ}=-145^{\circ}\)
\(\textbf{10)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=-150^{\circ}\)
The answer is \(210^{\circ},\,-510^{\circ}\)
\(\,\,\,\,\,-150^{\circ}+360^{\circ}=210^{\circ}\)
\(\,\,\,\,\,-150^{\circ}-360^{\circ}=-510^{\circ}\)
\(\textbf{11)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=330^{\circ}\)
The answer is \(690^{\circ},\,-30^{\circ}\)
\(\,\,\,\,\,330^{\circ}+360^{\circ}=690^{\circ}\)
\(\,\,\,\,\,330^{\circ}-360^{\circ}=-30^{\circ}\)
\(\textbf{12)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{5\pi}{6}\)
The answer is \(\frac{17\pi}{6},\,-\frac{7\pi}{6}\)
\(\,\,\,\,\,x=\frac{5\pi}{6} + 2\pi = \frac{5\pi}{6} + \frac{12\pi}{6} = \frac{17\pi}{6}\)
\(\,\,\,\,\,x=\frac{5\pi}{6} – 2\pi = \frac{5\pi}{6} – \frac{12\pi}{6} = -\frac{7\pi}{6}\)
\(\textbf{13)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{2\pi}{5}\)
The answer is \(\frac{12\pi}{5},\,-\frac{8\pi}{5}\)
\(\,\,\,\,\,x=\frac{2\pi}{5} + 2\pi = \frac{2\pi}{5} + \frac{10\pi}{5} = \frac{12\pi}{5}\)
\(\,\,\,\,\,x=\frac{2\pi}{5} – 2\pi = \frac{2\pi}{5} – \frac{10\pi}{5} = -\frac{8\pi}{5}\)
\(\textbf{14)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{11\pi}{9}\)
The answer is \(\frac{29\pi}{9},\,-\frac{7\pi}{9}\)
\(\,\,\,\,\,x=\frac{11\pi}{9} + 2\pi = \frac{11\pi}{9} + \frac{18\pi}{9} = \frac{29\pi}{9}\)
\(\,\,\,\,\,x=\frac{11\pi}{9} – 2\pi = \frac{11\pi}{9} – \frac{18\pi}{9} = -\frac{7\pi}{9}\)
\(\textbf{15)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{4\pi}{11}\)
The answer is \(\frac{26\pi}{11},\,-\frac{18\pi}{11}\)
\(\,\,\,\,\,x=\frac{4\pi}{11} + 2\pi = \frac{4\pi}{11} + \frac{22\pi}{11} = \frac{26\pi}{11}\)
\(\,\,\,\,\,x=\frac{4\pi}{11} – 2\pi = \frac{4\pi}{11} – \frac{22\pi}{11} = -\frac{18\pi}{11}\)
\(\textbf{16)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{9\pi}{8}\)
The answer is \(\frac{25\pi}{8},\,-\frac{7\pi}{8}\)
\(\,\,\,\,\,x=\frac{9\pi}{8} + 2\pi = \frac{9\pi}{8} + \frac{16\pi}{8} = \frac{25\pi}{8}\)
\(\,\,\,\,\,x=\frac{9\pi}{8} – 2\pi = \frac{9\pi}{8} – \frac{16\pi}{8} = -\frac{7\pi}{8}\)
See Related Pages\(\)
In Summary
Coterminal angles are two or more angles that share the same initial and terminal sides and differ only in the degree measure. In degrees, coterminal angles are angles that differ by a multiple of \(360\) degrees. In radians, coterminal angles differ by a multiple of \(2π\) radians.