Download 1.1 Radian and Degree Measure

1.1 Radian and Degree Measure.notebook
Trigonometry: The study of triangles
Unit 1 Lesson 1: Radian and Degree Measures
In pre-calculus, we use the study of triangles to further our study on angles and circles.
Important terms:
Angle: determined by rotating a ray about its endpoint.
Initial side: The starting ray
Terminal side: The side that rotates about the fixed point
Standard position: when the initial side of a ray coincides with the positive x-axis.
What you should learn:
What are radians and how do I convert between radians and degrees?
How do I use angles to model and solve real-life problems?
Why you should learn it: Radian measures are involved in numerous aspects of
our daily lives including work with angles, trigonometry, calculus, architecture, and
engineering.
How many degrees would be in a total rotation (from the positive x-axis all the way back around)?
y
Positive angles: generated by counterclockwise rotation.
How many degrees would be in half of a rotation?
Negative angles: generated by clockwise rotation.
A fourth?
x
y
A sixth?
An eighth?
A twelfth?
x
1.1 Radian and Degree Measure.notebook
Radian Measure
One radian is the measure of the central angle created when the arc length and radius are of equal
length.
One complete rotation in radians is
II
I
units.
So, 1/2 revolution =
=
1/4 revolution =
=
________ degrees
________ degrees
1/6 revolution =
=
________ degrees
III
IV
Coterminal Angles
Converting from Degrees to Radians
Two angles are coterminal when they have the same initial and terminal sides.
angle, always subtract
from the original angle.
Ex. 0 and 2
To find a coterminal
y
If
and
Finding and Sketching Coterminal Angles
Ex. Find the coterminal angle and sketch.
x
To convert degrees to radians, multiply degrees by
To convert radians to degrees, multiply radians by
Ex. Find the coterminal angle and sketch.
Ex. Find the coterminal angle and sketch.
** For negative angles, ADD
to find the coterminal angle!
1.1 Radian and Degree Measure.notebook
Ex. Convert Degree Measures to Radians and Sketch.
Ex. Convert from Radians to Degrees and sketch.
y
y
a. 135
b. 540
a.
x
x
b.
c. -270
c.
Complementary and Supplementary Angles
You better remember what these are! (At least those of you that had me for geometry!!)
Ex. Find the complement and supplement of each angle.
a. 72 degrees
b.148 degrees
c.
d.