13.2 Angles of Rotation

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13.2 Angles of Rotation

• Unit Circle Quiz May 11
• Ch. 13 Test May 13

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Do you recall

• In geometry, an angle is defined by two rays that
  have a common endpoint.
• In trig, an angle is defined by a ray that is
  rotated around the endpointthis is called ANGLE
  OF ROTATION.
• The Greek letter theta, T, is commonly used to
  name an angle of rotation.
• The starting position is the Initial Side and the
  final position is the TERMINAL SIDE.
• When the endpoint is at the origin, it is called
  STANDARD POSITION.

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What else?

• If rotated COUNTERCLOCKWISE- the angle has a
  positive measure
• If rotated CLOCKWISE-the angle has a negative
  measure
• The most common unit for angle measure is the
  degree.
• A complete rotation is 360 degrees, so 45 degrees
  is 1/8th of a complete rotation.
• (hintdivide)

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COTERMINAL

• Two angles are co-terminal if they have the same
  terminal side.
• What is co-terminal with 230 degrees?
• You can find the co-terminal angles by adding or
  subtracting integer multiples of 360o.

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Example

• Find the coterminal angle, ?, for each angle
  below such that -360olt?lt360o.
• 180o
• -27o

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Reference Angles

• For an angle in standard position, the reference
  angle, Tref , is the positive acute angle formed
  by the terminal side and the x-axis.

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Example

• Find the reference angle for
• 94 degrees
• 245 degrees
• 290 degrees
• -110 degrees

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Trig Functions

• Let P(x,y) be a point on the terminal side in
  standard position. The distance from the origin
  to P is

r
y
x
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Example

• Let P(-2,-3) by a point on the terminal side in
  standard position. Find the exact values of the 6
  trig functions.

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Lets make you think

• The terminal side of T in standard form is in
  Quadrant II and cos T -3/5. Find the exact
  values of the 6 trig functions.

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Practicing Helps You Remember

• P. 841 9 63 odd