529 5.1 Angles (b) 34.817° = 34° + 0.817° Write as a sum. = 34° + 0.817160′2 0.817° # 60′ 1° = 0.817160′2 = 34° + 49.02′ Multiply. = 34° + 49′ + 0.02′ Write 49.02′ as a sum. = 34° + 49′ + 0.02160″2 0.02′ # 60″ 1′ = 0.02160″2 = 34° + 49′ + 1.2″ Multiply. ≈34° 49′ 01″ Approximate to the nearest second. S Now Try Exercises 61 and 71. This screen shows how the TI-84 Plus performs the conversions in Example 4. The N DMS option is found in the ANGLE Menu. Standard Position An angle is in standard position if its vertex is at the origin and its initial side lies on the positive x-axis. The angles in Figures 8(a) and 8(b) are in standard position. An angle in standard position is said to lie in the quadrant in which its terminal side lies. An acute angle is in quadrant I (Figure 8(a)) and an obtuse angle is in quadrant II (Figure 8(b)). Figure 8(c) shows ranges of angle measures for each quadrant when 0° 6u 6360°. Coterminal Angles A complete rotation of a ray results in an angle measuring 360°. By continuing the rotation, angles of measure larger than 360° can be produced. The angles in Figure 9 with measures 60° and 420° have the same initial side and the same terminal side, but different amounts of rotation. Such angles are coterminal angles. Their measures differ by a multiple of 360°. As shown in Figure 10, angles with measures 110° and 830° are coterminal. Quadrantal Angles Angles in standard position whose terminal sides lie on the x-axis or y-axis, such as angles with measures 90°, 180°, 270°, and so on, are quadrantal angles. 0 x y 60° 420° Coterminal angles Figure 9 0 x y 110° 830° Coterminal angles Figure 10 x y 0 Q II 160° (b) 0° 360° 180° 90° 270° Q II 90°< u < 180° Q I 0°< u < 90° Q III 180°< u < 270° Q IV 270°< u < 360° (c) 0 x y Terminal side Vertex Initial side Q I 50° (a) Figure 8 Angles in standard position
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