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

2

3

2( 360 )

3

11

6

= 660°11

(360 )6

1 = 60 = 3600

Degrees Minutes Seconds60 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) 4040 5 in decimal places

1 140 5 40 40 5 40.668

60 3600

b) 50.525 in deg-min-sec60

50 .525 50 31.51

6050 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

(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°360

18h12h

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 12:0012(6) = 72°

108° + 6° = 114°

360

60

short hand (hour) is not right at 6!

It is of the way to 712 1

60 5

1(360 ) 30

12 Between hour 6 and hour 7 is

so… 1

(30 ) 65

72°

6°180° – 72° = 108°

Homework

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