1. Trigonometry
The Measure of triangles.

2. Measuring Angles
 The most common unit to measure
angles is the degree (1o).
 The degree is subdivided into 60 equal
parts known as minutes (1’).
 The minute is subdivided into 60 equal
parts known as seconds (1”).

3. Measuring Angles
1 degree = 60 minutes
 1 minute = 60 seconds
 1 degree = 3600 seconds

4. Measuring Angles
Convert to degrees, Convert to degrees:
minutes and  35o 12’ 7”
seconds:
 35o + 12’ (1o /60’) + 7”
 329.125o
(1o/3600”)
 3290 + (.125 x 60)’
 about 35.202o
 329o + 7.5’
 329o + 7’ + (.5 x 60)”
 329o + 7’ + 30”
 329o 7’ 30”

5. Terminal Side
Vertex
Initial Side

6. Central Angle
 An angle with its vertex at the center of a
circle.

7. Standard Position
 An angle with its vertex at the origin.
 The initial side lies along the positive
x-axis.

8. Radian Measure
 A central angle of a circle has a measure
of 1 radian if it intercepts an arc with
same length as the radius.

9. Measuring Angles
Degrees Radians

10. Circular Arc Length
 s=rθ
 The central angle θ is always a radian
measure.
 If it is not you must convert it to a radian
measure.