7-1 Measurement of Angles
Definitions
1) Angle - two rays joined at a common point called a vertex point.
Demo: Ferris Wheel (Manipula Math)
2) Revolution - a common unit used to
measure large angles, like the number of revolutions a car wheel makes
traveling at 10 mph.
3)
Degree - a common unit used to measure smaller angles. There
are 360 degrees in 1 revolution. 1/2 of a revolution = 180 degrees,
1/4 rev = 90o
Degrees can be
divided into smaller units of minutes and seconds. 1 degree equals
60 minutes, while 1 minute equals 60 seconds.
Examples
15.4o = 15o
+ .4(60)' = 15o 24'
50o30''15"
= 50o + (30/60)o + (15/3600)o = 50.5042o
4)
Radian - the measure of a the central angle when an arc of a circle has
the same length as the radius of the circle.
5)
Radian measure - the number of radius units in the length of an arc AB
s = r0
Changing radians to degrees
and degrees to radians.
To change degrees to
radians, multiply by p/180
310o
= 310 x p
/180 = 31 p/18
rads
To change radians to
degrees, multiply by 180/p
3p
= 3px 180/p = 540o
5 rads = 5 x 180/p
=286.5o
Angles in the co-ordinate
system
An angle in the co-ordinate system is usually placed in standard
position. This means that the vertex
is at the origin and its initial ray is along the positive x-axis.
A counterclockwise rotation
is considered to be positive
and a clockwise rotation
is considered to be negative.
If the terminal side of an angle is standard position lies
along an axis, the angle is said to be a qadranutal
angle. Two angles in standard postion
are called coterminal
if they have the same terminal side.
Samples
1) Find two angles with the same terminal
side, one positive and one negative for each angle.
a) 120o
Add 360 to find another positive 120 + 360 = 480o
Subtract 360 to find a negative 120 - 360 = -240o
b) 400o
Add or subtract 360 for a positive. 400 - 360 = 40o
Subtract enough 360's to make it negative. 400 - 360 - 360 =
-320o
