TOPIC: Measurement of Angles
TOPIC: Measurement of Angles
An angle is said to be in standard position if
1) its vertex is at the origin
2) its initial side is on the positive x-axis.
terminal
side
[pic]
initial side
A counterclockwise rotation represents a positive angle.
A clockwise rotation represents a negative angle.
The amount of rotation is measured in degrees or radians.
DEGREE MEASURE
1 degree = [pic] of a rotation.
Acute angle=_____________________________________
Right angle=_____________________________________
Obtuse angle=____________________________________
Straight angle=____________________________________
RADIAN MEASURE:
The radian measure of an (AOB is the number of radius units in the length of arc AB
[pic]
[pic]=[pic]
1. Find [pic] in radians. 2. So, if s = r, find [pic].
[pic]
[pic] = [pic]
3. Convert - 225( to radians. Leave in terms of (.
4. Convert 200( to radians. Round to three decimal places.
5. Convert -(/3 to degrees.
6. Convert 3.41 radians. Round to the nearest tenth of a degree.
Find the complement or supplement of each angle.
7. Find the complement of a 46[pic] angle.
8. Find the supplement of a 124[pic] angle.
9. Find the complement of [pic].
10. Find the complement of [pic].
11. Find the supplement of [pic].
12. Find the supplement of [pic].
13. Find the complement of [pic].
Sketch these angles:
1. Sketch a 120( angle, - 120( angle
2. Sketch a [pic] radians angle, - [pic] radians angle
-----------------------
N1-1
[pic]
A
s
r
B
s
3
r
2
1 radian = measure of a central angle whose arc has length r.
Formulas:
Degrees to Radians:
Radians to Degrees:
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