3.1 Radian Measure

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3.1 Radian Measure

• Objectives
• Radian measure.
• Converting between Degrees and Radians.
• Finding Function Values for Angles in Radians.
• Page 83

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• Since a radian is defined as a ratio of two
  lengths, the units cancel and the measure is
  considered unit-less.
• Therefore, if an angle measure is written with no
  degree symbol, it is assumed to be in radians.
• Though it is not essential, it is often customary
  to write radians or rads after an input measured
  in radians, especially when doing conversions and
  canceling units.

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• In many applications of trigonometry, radian
  measure is preferred over degree measure because
  it simplifies calculation and allows us to use
  the set of real numbers as the domain of the trig
  functions rather than just angles.

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Converting Standard Angles Between Degrees and
Radians
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Example 1
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Example 2
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You should memorize the following diagram.
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You should memorize the following table.
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Homework Assignment on the Internet

• Section 3.1(Read) Pp 107-109
• 1-4all, 6,8,12,14,22-38even, 46, 48, 52, 58, 62,
  66, 68,74,75.

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3.2 Application of Radian Measure

• Objectives
• Arc Length of a Circle.
• Sector of a Circle.
• Page 109

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Arc Length

• The length (s) of the arc intercepted on a circle
  of radius (r) by a central angle ? (measured in
  radians) is given by the product of the radius
  and the angle, i.e.,
• s r?.
• Caution ? must be in radians to use this
  formula.

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Example 1

• Find the length of the arc intercepted by a
  central angle ? 135o in a circle of radius r
  71.9 cm.

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Example 2

• Find the distance in kilometers between
  Farmersville, California, 36 N, and Penticton,
  British Columbia, 49 N, assuming they lie on the
  same north-south line. The radius of the earth is
  6400 km.

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Example 3

• A small gear and a large gear are meshed. An
  80.0 rotation of the smaller gear causes the
  larger gear to rotate 50.0 . Find the radius of
  the larger gear if the smaller gear has a radius
  of 11.7 cm.

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Area of a Sector of a Circle

• A sector of a circle is the portion of the
  interior of the circle intercepted by a central
  angle.

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Example 4
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Example 5

• The Ford Model A, built from 1928 to 1931, had a
  single windshield wiper on the drivers side. The
  total arm and blade was 10 inches long and
  rotated back and forth through an angle of 95.
  If the wiper blade was 7 inches, how many square
  inches of the windshield did the blade clean?

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Homework Assignment on the Internet

• Section 3.2(Read) Pp 113-117 2-6even, 10, 12,
  16, 20, 24, 26, 28, 36, 38, 40, 44-50 even.