Transcript Ch 14 Trigonometry!! 14.1 The unit circle

Ch 14 Trigonometry!!
Ch 14 Trigonometry!!
14.1 The unit circle
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Circumference
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Arc length
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Central angle
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In Geometry, our definition of an angle was
the union of two rays with a common
endpoint.
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Angle (trig) - measure of rotation from initial ray to
terminal ray
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initial ray - the positive x-axis with endpoint at origin
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terminal ray – ray with endpoint at origin
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standard position – initial ray is the x-axis so we only
need to show the terminal ray and the rotation.
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Counterclockwise rotation is “+”.
Clockwise rotation is “-”.
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Coterminal angles are angles in standard position with
the same terminal ray.
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Unit circle: A circle with center at the origin and a
radius of 1.
- Draw the unit circle
- Draw the following angles (degrees) in
standard position.
a) 45°
b) 135°
c) -45°
d) -225°
1) Find the length of the arc on the unit circle
formed by a 135 degree angle.
2) The terminal side of an angle contains the
point (5, -5). Find the measure of the angle.
3) Find the point of intersection of the unit
circle and the angle whose terminal side
contains the point (-7, -24).
4) The line
y
9
x
40
intersects the unit circle in
the second quadrant. Find the point of
intersection.