4.1
Angles and Radian Measure
By the end of class today I will be able to:
sketch an angle in standard position
find co­terminal angles
side
l
a
n
i
m
r
te
change between radians and degrees
Angle
Angle in Standard Position
x
tr e initial side
Ve
Positive angles rotate counterclockwise.
Negative angles rotate clockwise.
In a full rotation there are 360o or 2π
Quadrantal angles have the terminal side along the x or y axis (angle measures are multiples of 90° or π/2)
Label the quadrantal angles going counterclockwise (positive) and clockwise (negative)
Coterminal angles have the same terminal side when in standard position.
to generate coterminal angles, add or subtract multiples of 360o or 2π
Sketch each angle in standard position. State a positive and a negative coterminal angle for each.
110°
­160°
Positive:
Positive:
Negative:
Negative:
One radian: the measure of the central angle (θ) whose intercepted arc is the same length as the radius (r).
360o=2π radians
180o=π radians
Conversion Factors
radian to degrees
degrees to radian
π
180o
180o
π
convert 260o to radians
convert 2π to degrees
3
When sketching angles that are outside of 0≤θ≤306 or 0≤θ≤2π, you
may find it helpful to add or subtract to find the coterminal angle in
that angle range.
Sketch the angles in standard position
π
­5π 4π
4
6
3
7π 4
11π
12
-5π
3
page 505
problems 17-20, 32-36, 41-46, 58, 62, 65, 68