4.1 Radian and Degree Measure

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4.1 Radian and Degree Measure
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Objective

• To use degree and radian measure.

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Angles

• An angle is determined by rotating a ray about
  its endpoint.
• The starting point of the ray is the initial
  side.
• The ending position is the terminal side.

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Angles

• The endpoint of the ray is called the vertex of
  the angle.
• An angle in standard position has its initial
  side on the positive x-axis and its vertex at the
  origin.

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Angles

• If the rotation of the ray is counterclockwise
  the angle has positive measure.
• If the rotation of the ray is clockwise the angle
  has negative measure.

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Angles

• An angle in standard position is said to lie in
  the quadrant in which its terminal side lies.
• A central angle of a circle is an angle whose
  vertex is on the center of the circle.

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Degree Measure

• An angle generated by one complete
  counterclockwise rotation measures 360.
• One generated by a complete clockwise rotation
  measures -360.

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Coterminal angles

• Angles that have the same initial and terminal
  sides are called coterminal.

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Radian Measure

• The measure of an angle is determined by the
  amount of rotation from the initial side to the
  terminal side.

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Definition of a Radian

• One radian is the measure of a central angle ?
  that intercepts an arc s equal in length to the
  radius r of the circle. Algebraically this means
  that ? s / r where ? is measured in radians.

Radian Demo http//id.mind.net/zona/mmts/trigonom
etryRealms/radianDemo1/RadianDemo1.html
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• The circumference of a circle is 2pr. There are
  2p radians around the circumference of a circle.
  
• There are about 6.28 radians in a full circle.

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• 1 radians 57.29
• 1 degree 0.017 radians

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• To convert degrees to radians
• To convert radians to degrees

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• When no units of angle measure are specified,
  radian measure is implied.

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ExampleConverting from Degrees to Radians

• 135 3p/4
• 540 3p
• -270 -3p/2

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ExampleConverting from Radians to Degrees
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