In Exercises dmsfirst - dmslast, convert the angles into the DMS system. Round each of your answers to the nearest second.
\(63.75^{\circ }\)

\(63^{\circ } 45'\)
\(200.325^{\circ }\) \(=\) \(\answer {200}\) degrees \((^{\circ })\) \(\answer {19}\) minutes \((')\) \(\answer {30}\) seconds \(('')\)
\(-317.06^{\circ }\)

\(-317^{\circ } 3' 36''\)
\(179.999^{\circ }\) \(=\) \(\answer {179}\) degrees \((^{\circ })\) \(\answer {59}\) minutes \((')\) \(\answer {56}\) seconds \(('')\)
In Exercises decimaldegfirst - decimaldeglast, convert the angles into decimal degrees. Round each of your answers to three decimal places.
\(125^{\circ } 50'\)

\(125.833^{\circ }\)
\(-32^{\circ } 10' 12'' = \answer {-32.170}\) degrees \((^{\circ })\)
\(502^{\circ } 35'\)

\(502.583^{\circ }\)
\(237^{\circ } 58' 43'' = \answer {237.979}\) degrees \((^{\circ })\)
In Exercises orientedanglefirst - orientedanglelast, graph the oriented angle in standard position. Classify each angle according to where its terminal side lies and then give two coterminal angles, one of which is positive and the other negative.
\(30^{\circ }\)

\(30^{\circ }\) is a Quadrant I angle which is coterminal with \(390^{\circ }\) and \(-330^{\circ }\)

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\(120^{\circ }\)

\(120^{\circ }\) is a Quadrant II angle which is coterminal with \(480^{\circ }\) and \(-240^{\circ }\)

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\(225^{\circ }\)

\(225^{\circ }\) is a Quadrant III angle which is coterminal with \(585^{\circ }\) and \(-135^{\circ }\)

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\(330^{\circ }\)

\(330^{\circ }\) is a Quadrant IV angle which is coterminal with \(690^{\circ }\) and \(-30^{\circ }\)

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\(-30^{\circ }\)

\(-30^{\circ }\) is a Quadrant IV angle which is coterminal with \(330^{\circ }\) and \(-390^{\circ }\)

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\(-135^{\circ }\)

\(-135^{\circ }\) is a Quadrant III angle which is coterminal with \(225^{\circ }\) and \(-495^{\circ }\)

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\(-240^{\circ }\)

\(-240^{\circ }\) is a Quadrant II angle which is coterminal with \(120^{\circ }\) and \(-600^{\circ }\)

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\(-270^{\circ }\)

\(-270^{\circ }\) is a quadrantal angle shich is coterminal with \(90^{\circ }\) and \(-630^{\circ }\)

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\(405^{\circ }\)

\(405^{\circ }\) is a Quadrant I angle which os coterminal with \(45^{\circ }\) and \(-315^{\circ }\)

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\(840^{\circ }\)

\(840^{\circ }\) is a Quadrant II angle which is coterminal with \(120^{\circ }\) and \(-240^{\circ }\)

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\(-510^{\circ }\)

\(-510^{\circ }\) is a Quadrant III angle which is coterminal with \(-150^{\circ }\) and \(210^{\circ }\)

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\(-900^{\circ }\)

\(-900^{\circ }\) is a quadrantal angle which is coterminal with \(-180^{\circ }\) and \(180^{\circ }\)

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With help from your classmates, explain why if \((x,y)\) is a point on the terminal side of an angle \(\alpha \) in standard position, then so is \((r\,x, r\,y)\) for any number \(r > 0\). What happens if \(r < 0\)?