Download U6_2 L0 Pre-requisite skills

UNIT 6: Prerequisite Skills
LESSON 0
Math Course 3
Adv. Alg. w/Trig.
ANGLES AND ANGLE MEASURE
There are two commonly used units of measurement for angles – degrees and radians. The more
familiar unit of measurement is that of degrees. Degrees may be further divided into minutes and
seconds as seen in the previous lesson 0.1.
Angle - two rays joined at a common point called a vertex point.
Standard position
On a coordinate plane, an angle may be generated by rotation of two rays that share common vertex at
the origin. One ray called the initial side is fixed along the x-axis. The other ray called the terminal
side rotates about the center. An angle is in standard position when its vertex A is at the origin of the x-y
plane, and its Initial side AB lies along the positive x-axis, while its Terminal side AC has rotated.
The measure of an angle is determined by the amount of rotation of the terminal side. If the rotation is in
a counterclockwise direction, the measure of the angle is positive. If the rotation is in a clockwise
direction, the measure of the angle is negative.
If you graph a 390° angle and a 30° angle in standard position on the same coordinate plane,
you will notice that the terminal side of the 390° angle is the same as the terminal side
of the 30° angle. When two angles in standard position have the same terminal sides, t
hey are called coterminal angles.
Notice that 390° - 30° = 360°. In degree measure, coterminal angles differ by
an integral multiple of 360°. You can find an angle that is coterminal to a given angle by
adding or subtracting a multiple of 360°. In radian measure, a coterminal angle is found by adding or subtracting a multiple of 2π. (radian
measure is introduced in the next lesson 0.3)
Radian Measure
Radians are another way to measure angles. They are more practice in real world problem solving.
The definition of a radian is based on the concept of a unit circle. Unit circle is a circle on the coordinate plane with radius that is 1 unit. The
radian measure of an angle is based on the length of an arc on the unit circle.
The circumference of a circle is C = 2r.
Since radius of the unit circle = 1 unit , then C = 2(1)
Half a circle, then, is π. And, each right angle is ½ of π or
Three right angles (270°) will be 3    3  etc.
2
2
 C = 2

2
As with degrees, the measure of an angle in radians is positive if its rotation is counterclockwise. The measure is negative if the rotation is
clockwise.
IMPORTANT CONVERSIONS TO REMEMBER:
When converting between the two measurement systems, use the proportions:
OR
 To convert from degrees to radians: multiply the degree measure by π/ 180.
Example
60º is equal to
60



 radians  1.05 radians
1 180 3
 To convert from radians to degrees: multiply the degree measure by 180/ π.
Example

4
is equal to

4

180

 45
Or for some problems, just think about the problem

4
is ½ of

2


2
is a right angle 90°, and so

4
= 45°