### 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) rotation clockwise 3 2 = –240° 3 11 b) rotation counterclockwise 6 11 6  = 660°

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 b) 50.525

5 40 in decimal places 1  40  60    1  3600    40.668

 in deg-min-sec .525

 60  31.5

 31 .5

60  31 30 50 31 30

Ex 3) Identify all angles coterminal with –450 coterminal angle whose measure is between 0 & find the & 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?

18h    360  12 h    = 540°

Ex 5) What is the measure in degrees of the smaller of the angles formed by the hands of a clock at 6:12?

72° long hand (minute) at :12 so each minute is    360  60    = 6°  from 12:00 12(6 ) = 72° short hand (hour) is not right at 6!

6° 180° – 72° = 108°

12 1 It is of the way to 7 60  5 1 Between hour 6 and hour 7 is 12 108° + 6° = 114° so… 1 5 6 30

### Homework

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