3.1 Angles in the Coordinate Plane

Positive We can measure angles in degrees Negative   initial side terminal side 360   once around

Ex 1) Find the degree measure of the angle for each given rotation & draw angle in standard position. a) rotation clockwise = –240° b) rotation counterclockwise = 660°

1  = 60 = 3600  Degrees  Minutes  Seconds 60 minutes in 1 degree/ 60 seconds in 1 minute * 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 b)  in deg-min-sec

Ex 3) Identify all angles coterminal with –450  & find the coterminal angle whose measure is between 0  & 360  (k is an integer) –450  + 360° = – 90° –450  + 360°k –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? = 540°

long hand (minute) at :12 so each minute is Ex 5) What is the measure in degrees of the smaller of the angles formed by the hands of a clock at 6:12? = 6°  from 12:00 12(6  ) = 72° 108° + 6° = 114° short hand (hour) is not right at 6! It is of the way to 7 Between hour 6 and hour 7 is so… 72° 6° 180° – 72° = 108°

Homework #301 Pg 123 #1, 5, 7, 9, 15–31 odd, 32–39, 41, 43, 45, 47