Angles and Their Measure—Section
6.1—Day 1
Angles and angle measure are essential
to trigonometry. In algebra we used (x, y)
coordinates to
identify the position of a point. In
trigonometry we
use direction (angle) and distance to
identify position. We also use Greek letters, like  (alpha) (beta)and  (theta)
to name angles. Describing angles is essential, and learning some Greek is
important too! Complete this Vocabulary Activity -- due on Tuesday. Also
complete the Angle Measure Assignment that we started in class.
Advise: Use a highlighter when reading, and look up (online of course!) every
word you do not know. Practice vocabulary using flashcards (online or using real
cards) now and throughout the course. Make sure you can use a protractor and
ruler to draw diagrams that accurately represent problems.
Goal: Understand and memorize the vocabulary of angles. Learn to use your
measurement tools.
Coterminal angles You can go around a circle forever, and each time you pass a
specific angle, you have added one more revolution to your spin. Coterminal
angles have different measure, but end in the same place. This kind of numbering
is exactly what we need to describe ALL behavior that repeats (like sunrise,
heartbeat, breath, orbits etc.) . . . TRIGONOMETRY with coterminal angles is
POWERFUL!
Advise: Study page 480 in your book while using this animation of coterminal
angles angles.
Goal: Know how to determine coterminal angles and simplify to the smallest
positive (or negative) angle measure.
Degree Measure was invented by the Babylonians before 1600 BCE. In degree
measure a complete revolution is 360 With so many factors, 360 gives easy
angle measures for many fractions of a circle. For this reason degree measure is
still with us.
Degrees, Minutes and Seconds (dms):
Whenever accuracy is important, decimal
portions of a degree can be rewritten using
minutes and seconds. Minutes are sixtieths of
a degree, and seconds are sixtieths of a minute.
Read examples 2 to 5 on pages 481 and 482,
and practice here. Your calculator has a DMS
function and this video, (starting at 1:53 minutes), has a good description of
just how to use your calculator.
Advise: Practice using your calculator angle features for this. Make sure you
know that your answer is reasonable. You will not be asked to do this by
hand, and you must be able to convert quickly.
Goal: Read, use and convert between decimal degrees and dms.
Radian Measure are used to simplify formulas for circular arcs, sectors of circles
and circular motion. One radian is the angle created by wrapping one radius along
the circumference of its circle.
Advise: Study the definition and description on page 482 and use this animation to
see the radian measure for each radian.
Converting between Degrees and Radians
Often we will want to convert angle measure. Because 360
radians,
180
degrees is π radians. We use this fact as a conversion factor:
(Degrees)
= Radians
(Radians)
= Degrees
Advise: Study page 483, use this spreadsheet for the “must know” angles,
and practice these conversions. Use the Math Lab Study Plan
or your book.
Goal: Convert between radian and degree measure automatically.