Download Lesson 3.1 Angles in the Coordinate Plane notes

3.1 Angles in the Coordinate Plane
Trigonometry comes from the Greek words trigonon (triangle) and metron (measure). Two
fundamental concepts needed for the study of trigonometry are angle and angle measure.
In trigonometry, an angle is formed by rotating a ray about its endpoint. The initial side of the angle
is the starting position of the ray and the terminal side is its ending position.
y
II
I
terminal side
x
vertex
initial side
III
IV
An angle in standard position has its initial side on the positive x-axis and its vertex at the origin.
The measure of an angle describes the amount of rotation required to get from the initial side to the
terminal side. If the rotation is counterclockwise, the angle has positive measure. If the rotation is
clockwise, the angle has negative measure.
An angle can be measured in degrees or in radians.
An angle generated by one complete counterclockwise rotation measures 360 or 2 radians.
y
360
x
An angle generated by one complete clockwise rotation measures -360 or -2 radians.
y
-360
x
Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane
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Example 1: Find the degree measure of the angle for each given rotation and draw the angle in
standard position.
a.
3
rotation, counterclockwise
4
y
x
b.
1
rotation, clockwise
2
y
x
c. 2
1
rotation, counterclockwise
3
y
x
Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane
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d.
7
rotation, clockwise
6
y
x
e.
2
rotation, clockwise
3
y
x
f.
11
rotation, counterclockwise
6
y
x
Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane
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Example 2: The earth completes one rotation on its axis every 24 hours. Through how many degrees
does a point on earth rotate in:
a. 8 hrs
b. 7 days
c. 12 hrs
d. 5 days
e. 18 hrs
f. 11 days
The hour hand on a clock makes one rotation in 12 hours. Through how many degrees does the hour
hand rotate in:
g. 9 hrs
h. 18 hrs
Degrees may be divided into smaller parts by using decimals or by using minutes and seconds. Each
degree is divided into 60 minutes (′) and each minute is divided into 60 seconds (″).
Example 3: Express:
a. 3650′10″ in decimal degrees
b. 4040′5″ in decimal degrees
c. 50.525 in degrees-minutes-seconds
d. 15.345 in degrees-minutes-seconds
Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane
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Coterminal angles are angles of different measures with the same terminal side in standard position.
If  is the degree measure of an angle, then all angles coterminal with this angle have measure
 + 360k, where k is an integer.
Example 4: Identify all coterminal angles with the given angle whose measures are between 0 and
360.
a. -45
b. -200
c. -450
d. -750
e. -2100
Homework: p 123 => Class Exercises 1 – 8 (day 1)
pp. 123-124 => Practice Exercises 1 – 10; 14 – 23 (day 2)
Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane
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