Download Section 3.1 – Radian Measure

Section 3.1 – Radian Measure
Goals/Objectives – Tuesday March 2, 2010
1. To be able to describe the difference between a
radian and a degree
2. To be able to convert degrees to radians and vice
versa
3. To find the exact values of trigonometric functions
involving radian measure.
What are radians?
• Radian: an angle that is equal in measure to
the length of an arc of a circle.
– Remember arc length?
• Deals with circumference…what is circumference?
Circumference  2 radius
Why is this different than degree?
• The origin of a degree is not really known – it
is said that one full rotation of an angle in
standard position is 360 degrees because
there are almost 360 days in a year and it is
easier to divide up 360 degrees in equal
increments then it is 365 days.
Uses
• We use degrees in lower level mathematics
courses such as Geometry because of the ease
in which they can be manipulated.
• We use RADIAN measure in higher order
mathematics courses because it allows us to
treat the DOMAIN of a function as REAL
NUMBERS…
1 unit
If NO UNIT of an angle measure is specified, then the angle is
understood to be measured in RADIANS!
Conversions
0
180
1 radian =


1 =
0
180
0
Convert the following to Degrees…
9
4
5

6
Convert the following to radians…
0
45
249
0
The Special Angles
Degree
0
0
0
30
0
45
0
60
0
90
0
180
0
270
3600
Radian
Sine Value Cosine
Value
Tangent
Value
Find the exact value for the following…
2
tan
3
4
cos( )
3