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Trigonometry ANGLES OF ROTATION – SECTION 1.1 DAY 2 Getting ready for class What is meant by standard position for an angle? Given any angle, how do you find another angle that is coterminal to it? One complete revolution is ____ degrees. Solve the following problems and write the answers on a piece of paper. 1. It takes the earth 24 hours to make one complete revolution on its axis. Through how many degrees does the earth turn in 12 hours? In one hour? 2. A turntable in a shop makes 45 revolutions per minute. How many revolutions does it make per second? 3. A tire is rotating 15 rpm (revolutions per minute). How many degrees does it turn in 5 seconds? Angles of Rotation If two angles have a sum of 90⁰, then they are called complementary angles and we say each is the complement of the other. Two angles with a sum of 180⁰, are called supplementary angles and we say they are supplements of each other. Find the complement and the supplement of each angle. 1. 40⁰ 2. 110⁰ 3. 240⁰ 4. Θ Answers 1. complement 50⁰ supplement 140⁰ 2. C = -20⁰ S = 70⁰ 3. C = - 150⁰ S = -60⁰ 4. Complement 90⁰ – θ Supplement 180⁰– θ Find the measure of each marked angle Fractional parts of degrees With calculators it is convenient to use decimal degrees to denote fractional parts of degrees. Historically, however, fractional parts of degrees were expressed in minutes and seconds, using the prime ( ' ) and double prime( '' ) notations, respectively. Phrases like “minutes” and “seconds” are used to make a connection between time and the fraction of a degree that is associated with these phrases. 1' = one minute = (1/60)(1°) 1'' = one second = (1/60)(1') or (1/3600)(1°) Convert 64°32'4'' to decimal degree Every calculator has a different set of procedures for this task…hopefully you will use the same calculator all semester. Some scientific calculators have a button that says DMS → DD In that case, you enter the value as 64.3204 (even though it is not a decimal) then hit the DMS → DD button. 64.5344 Convert 64°32'4'' to decimal degree On a graphing calculator, ANGLE (option 1 is degree °) (option 2 is minute ') ALPHA (+) is '' ENTER 64. 5344 Additional Examples: Convert 120.6° to DMS On a scientific calculator use the DD→ DMS button. On a graphing calculator, go under the ANGLE menu (option 4) 120° 36' Convert -34.36° to DMS -34° 21' 36'' Additional problems: Find the complement and supplement of 20° 10' 30" Find one positive and one negative coterminal angle to 150° 40' 35"