*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 = 90*^{o}
* Degrees can
be
divided into smaller units of minutes and seconds. 1 degree
equals
60 minutes, while 1 minute equals 60 seconds.*
*Examples*
*15.4*^{o} =
15^{o}
+ .4(60)' = 15^{o} 24'
*50*^{o}30''15"
= 50^{o} + (30/60)^{o} + (15/3600)^{o} = 50.5042^{o}
*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 = r*~~0~~

*Changing radians to
degrees
and degrees to radians.*
* *
*To change degrees
to
radians, multiply by p/180*
*310*^{o}
= 310 x p
/180 = 31 p/18
rads
* *
*To change radians
to
degrees, multiply by 180/p*
* *
*3p
= 3px 180/p = 540*^{o}
*5 rads = 5 x 180/p
=286.5*^{o}

*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) 120*^{o}
*
Add 360 to find another positive 120 + 360 = 480*^{o }
*
Subtract 360 to find a negative 120 - 360 = -240*^{o}
* *
*
b) 400*^{o}
*
Add or subtract 360 for a positive. 400 - 360 = 40*^{o}
*
Subtract enough 360's to make it negative. 400 - 360 - 360 =*
*-320*^{o}

* *