### 3.1 Angles in the Coordinate Plane terminal side Positive initial side Negative We can measure angles in degrees  once around Ex 1) Find the degree measure of.

```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 
405  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
```