531 5.1 Angles This table shows some examples of coterminal quadrantal angles. Examples of Coterminal Quadrantal Angles Quadrantal Angle U Coterminal with U 0° {360°, {720° 90° -630°, -270°, 450° 180° -180°, 540°, 900° 270° -450°, -90°, 630° EXAMPLE 6 Analyzing Revolutions of a Disk Drive A constant angular velocity disk drive spins a disk at a constant speed. Suppose a disk makes 480 revolutions per min. Through how many degrees will a point on the edge of the disk move in 2 sec? SOLUTION The disk revolves 480 times in 1 min, or 480 60 times = 8 times per sec (because 60 sec = 1 min). In 2 sec, the disk will revolve 2 # 8 = 16 times. Each revolution is 360°, so in 2 sec a point on the edge of the disk will revolve 16 # 360° = 5760°. A unit analysis expression can also be used. 480 rev 1 min * 1 min 60 sec * 360° 1 rev * 2 sec = 5760° Divide out common units. S Now Try Exercise 123. 5.1 Exercises CONCEPT PREVIEWFill in the blank to correctly complete each sentence. 1. One degree, written 1°, represents _____ of a complete rotation. 2. If the measure of an angle is x°, its complement can be expressed as _____ - x°. 3. If the measure of an angle is x°, its supplement can be expressed as _____ - x°. 4. The measure of an angle that is its own complement is _____. 5. The measure of an angle that is its own supplement is _____. 6. One minute, written 1′, is _____ of a degree. 7. One second, written 1″, is _____ of a minute. 8. 12° 30′ written in decimal degrees is _____. 9. 55.25° written in degrees and minutes is _____. 10. If n represents any integer, then an expression representing all angles coterminal with 45° is 45° + _____. Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 11. 30° 12. 60° 13. 45° 14. 90° 15. 54° 16. 10° 17. 1° 18. 89° 19. 14° 20′ 20. 39° 50′ 21. 20° 10′ 30″ 22. 50° 40′ 50″
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