1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
The Unit Circle
EQ: How do I use special right triangles to
generalize?
May 5­10:32 AM
Vocabulary
Term
Definition or “How do I Find Example
It?”
An angle in Standard Position
When the vertex is at the origin and the initial side lies on the positive side of the x­
axis.
Initial Side
The ray of the angle that lies on the x­axis; it is where the angle is measured from.
Terminal Side
The resulting ray once the angle is rotated around the origin forms the other side of the angle.
Positive Angle
Produced when the terminal side is rotated counterclockwise around the origin. Negative Angle
Produced when the terminal side is rotated clockwise around the origin.
Coterminal Angles
Two angles are coterminal when they share the same terminal side.
Reference Angle
What is the reference angle for An acute angle between 0 120 degrees? and 90 degrees in relation to 295 degrees? 540 degrees? the x­axis
­80 degrees?
Name 2 coterminal angles for 75 degrees: May 5­10:40 AM
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1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
What is the circumference of a circle with
radius 1?
1
May 5­4:04 PM
What is a radian?
A radian is an angle measurement equal to the length of the arc it would create on a circle of radius 1 (unit circle). In a unit circle, the degree measurement goes between ___ and ___; the radian measurement goes between ___ and ___.
360o = 2π radians
or
o
180 = π radians
May 5­11:27 AM
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1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
Convert the following into radians.
1. 90o
2. 135o
3. 240o
May 5­3:58 PM
Convert the following into degrees.
1. π radians
2. 2π/3 radians
3. 4 radians
May 5­3:58 PM
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1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
Solve the following 30­60­90 triangle.
1
30
May 5­10:33 AM
Solve the following 45­45­90 triangle.
1
May 5­10:33 AM
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1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
The Unit Circle assumes a circle of radius 1 that is centered on your coordinate plane at the origin. A standard angle starts on the positive side of the x­axis.
Every point along the unit circle can be read as (cosθ, sinθ).
Tan θ can be calculated as y/x.
May 5­4:13 PM
A reference angle is an acute angle between 0o and 90o or 0 radians and π/2 radians. Every other quadrant uses the first quadrant as its reference angle based on the x­axis. It then changes the signs accordingly for the quadrant.
May 11­5:07 PM
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1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
First Quadrant:
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Second Quadrant:
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1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
Third Quadrant:
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Fourth Quadrant:
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1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
The Complete Unit Circle
May 5­4:16 PM
Coterminal Angles are angles whose initial and terminal sides coincide. These angles occur every 360o or 2π radians. They can be negative or positive and can be found by adding or subtracting 360o or 2π radians.
May 11­5:08 PM
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1 ­ Notes ­ The Unit Circle.notebook
May 12, 2015
Find the smallest positive and negative coterminal angle for the following angles. Then, find the reference angle.
1. 245o
4. 7π/3
2. ­520o
5. ­13π/6
3. ­2000o
6. ­25π/4
May 5­4:30 PM
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