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.
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Transcript 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
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
180° – 72° = 108°
of the way to 7
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