Angles of Rotation

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Angles of Rotation Section 1.1 Day 2

• Trigonometry

2
Getting ready for class

• What is meant by standard position for an angle?
• Given any angle, how do you find another angle
  that is coterminal to it?
• One complete revolution is ____ degrees.

3
Solve the following problems and write the
answers on a piece of paper.

• 1. It takes the earth 24 hours to make one
  complete revolution on its axis. Through how
  many degrees does the earth turn in 12 hours? In
  one hour?
• 2. A turntable in a shop makes 45 revolutions
  per minute. How many revolutions does it make
  per second?
• 3. A tire is rotating 15 rpm (revolutions per
  minute). How many degrees does it turn in 5
  seconds?

4
Angles of Rotation

• If two angles have a sum of 90, then they are
  called complementary angles and we say each is
  the complement of the other.
• Two angles with a sum of 180, are called
  supplementary angles and we say they are
  supplements of each other.

5
Find the complement and the supplement of each
angle.

• 40
• 2. 110
• 3. 240
• 4. T

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Answers

• complement 50
• supplement 140
• C -20
• S 70
• 3. C - 150
• S -60
• 4. Complement 90 ?
• Supplement 180 ?

7
Find the measure of each marked angle
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Fractional parts of degrees

• With calculators it is convenient to use decimal
  degrees to denote fractional parts of degrees.
• Historically, however, fractional parts of
  degrees were expressed in minutes and seconds,
  using the prime ( ' ) and double prime( '' )
  notations, respectively.

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• Phrases like minutes and seconds are used to
  make a connection between time and the fraction
  of a degree that is associated with these
  phrases.
• 1' one minute (1/60)(1)
• 1'' one second (1/60)(1') or
  (1/3600)(1)

10
Convert 6432'4'' to decimal degree

• Every calculator has a different set of
  procedures for this taskhopefully you will use
  the same calculator all semester.
• Some scientific calculators have a button that
  says DMS ? DD
• In that case, you enter the value as 64.3204
  (even though it is not a decimal) then hit the
  DMS ? DD button.
• 64.5344

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Convert 6432'4'' to decimal degree

• On a graphing calculator,
• ANGLE (option 1 is degree )
• (option 2 is minute ')
• ALPHA () is ''
• ENTER
• 64. 5344

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Additional Examples

• Convert 120.6 to DMS
• On a scientific calculator use the DD? DMS
  button.
• On a graphing calculator, go under the ANGLE
  menu (option 4)
• 120 36'

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Convert -34.36 to DMS

• -34 21' 36''

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Additional problems

• Find the complement and supplement of
• 20 10' 30"
• Find one positive and one negative coterminal
  angle to 150 40' 35"