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3.1 Angles in the Coordinate Plane terminal side Positive initial side Negative We can measure angles in degrees 360 once around Ex 1) Find the degree measure of the angle for each given rotation & draw angle in standard position. a) 2 rotation clockwise 3 2 (360) = –240° 3 b) 11 6 rotation counterclockwise 11 (360) = 660° 6 Degrees Minutes Seconds 60 minutes in 1 degree / 60 seconds in 1 minute 1 = 60 = 3600 * to figure out which ratio, think about what you are canceling – put that on bottom of fraction Ex 2) Express: a) 40 40 5 in decimal places 1 1 405 40 40 5 40.668 60 3600 b) 50.525 in deg-min-sec 60 50 .525 50 31.5 1 60 50 31 .5 50 31 30 50 31 30 1 Ex 3) Identify all angles coterminal with –450 & find the coterminal angle whose measure is between 0 & 360 –450 + 360°k (k is an integer) –450 + 360° = – 90° –450 + 720° = 270° Horology (having to do with time) Ex 4) The hour hand of the clock makes 1 rotation in 12 hours. Through how many degrees does the hour hand rotate in 18 hours? 360 18h = 540° 12h Ex 5) What is the measure in degrees of the smaller of the angles formed by the hands of a clock at 6:12? long hand (minute) at :12 so 72° 360 each minute is = 6° 60 from 12:00 12(6 ) = 72° short hand (hour) is not right at 6! 12 1 of the way to 7 180° – 72° = 108° It is 60 5 1 Between hour 6 and hour 7 is (360) 30 12 1 so… (30) 6 108° + 6° = 114° 5 6° Homework #301 Pg 123 #1, 5, 7, 9, 15–31 odd, 32–39, 41, 43, 45, 47