Intro to Trigonometry

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Intro to TrigonometryAngles
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Measurement of Angles

• The measure of an angle is the rotation from the
  initial ray to the terminal ray
• Standard Position of an Angle

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Misconceptions from Geometry

• What is the largest angle possible?
• What is the smallest angle possible?
• If rotation of angle is counterclockwise, then
  the angle is positive
• If rotation of angle is clockwise, then the angle
  is negative

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Estimate the measure of the angle below (Give a
positive and negative angle)
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How many degrees are in one revolution?

• Draw a 765 degree angle in standard position
• What are some other ways we could measure this
  angle?
• How is a 765 degree angle different than a 45
  degree angle?

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Co-Terminal Angles

• Two angles in standard position are coterminal
  angles if they have the same terminal ray
• Give a positive and negative coterminal angle for
  60 degrees

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Radian Measure of an Angle

• Radians are an angle measurement that represent a
  ratio between arc length and radius of a sector
• We commonly refer to the measure of the angle as
  (theta)
• Given the arc length (s), radius (r), and/or
  angle, we can say

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Converting Degrees to Radians and Radians to
Degrees

• What do we call it if you go all the way around a
  circle?
• What is the formula for this?
• Since we can say and..
• 1 Revolution radians

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Conversion Formulas
By solving for each side, we obtain the
formulas.
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Examples

• Convert from degrees to radians
• 90 2) 180 3) 270
• Convert from radians to degrees
• 1) 2) 3) 2

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Quadrants of the coordinate plane and the angles
that determine them
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Circular Motion

• A gear revolves at 40 rpm. Find the number of
  degrees per minute through which the gear turns
  and then find the number of radians through which
  the gear turns.

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• Homework
• Pg. 261 (1 13odd, 17, 19, 25, 27)