Chapter 4.3Trigonometry Extended: The Circular             Functions
Standard Position   An angle with its vertex at the origin.   The initial side lies along the positive    x-axis.
Quadrantal Angle   When the terminal side coincides with    one of the axes.                    900                      ...
Acute Angle   If the terminal side falls in the first    quadrant it is said to be an acute angle.   Generally talking a...
Obtuse Angle   If the terminal side falls in the second    quadrant it is said to be an obtuse angle.   Generally talkin...
Coterminal Angles   Two angles in standard position that    share the same terminal side.   Angles that differ by multip...
Reference Angle   For any angle α , 0o < α < 360o   The reference angle is the acute angle    formed by the terminal sid...
The Unit Circle A circle with a radius of 1 It’s center is at the origin Symmetric to the x-axis, the y-axis, and theorigin
Sine and Cosine Ifthe terminal side of an angle θ  in standard position intersects  the unit circle at P(x, y), then  cos...
Trig Functions of an Angle inStandard Position
Trig Functions of an Angle inStandard Position
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Lesson 4.3

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Lesson 4.3

  1. 1. Chapter 4.3Trigonometry Extended: The Circular Functions
  2. 2. Standard Position An angle with its vertex at the origin. The initial side lies along the positive x-axis.
  3. 3. Quadrantal Angle When the terminal side coincides with one of the axes. 900 00 or 1800 3600 2700
  4. 4. Acute Angle If the terminal side falls in the first quadrant it is said to be an acute angle. Generally talking about an angle formed in the normal way (standard position), positive or counter clock wise.
  5. 5. Obtuse Angle If the terminal side falls in the second quadrant it is said to be an obtuse angle. Generally talking about an angle formed in the normal way (standard position), positive or counter clock wise.
  6. 6. Coterminal Angles Two angles in standard position that share the same terminal side. Angles that differ by multiples of 3600. Every angle has infinitely many coterminal angles. (α + 360ko) α – angle k - integer
  7. 7. Reference Angle For any angle α , 0o < α < 360o The reference angle is the acute angle formed by the terminal side and the closest x-axis.
  8. 8. The Unit Circle A circle with a radius of 1 It’s center is at the origin Symmetric to the x-axis, the y-axis, and theorigin
  9. 9. Sine and Cosine Ifthe terminal side of an angle θ in standard position intersects the unit circle at P(x, y), then cos θ = x and sin θ = y. Sine and cosine always range between -1 and 1.
  10. 10. Trig Functions of an Angle inStandard Position
  11. 11. Trig Functions of an Angle inStandard Position

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