8.9 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Unit Circle | Obsidian::STEM | trigonometry |
|
Overview
On the cartesian, the unit circle is the circle with center at the origin and radius 1.
Suppose intervals [a, b] is mapped to an arc on the unit circle. Then the point on the unit circle corresponding to a is called the initial point of the arc. The point corresponding to b is called the terminal point of the arc.
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Basic
On the Cartesian coordinate system, what is the unit circle?
Back: The circle with center at the origin and radius 1.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
On the Cartesian coordinate system, where is the center of the unit circle located?
Back: At \langle 0, 0 \rangle, i.e. the origin.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
What is the radius of the unit circle?
Back: 1
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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What is the diameter of the unit circle?
Back: 2
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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What is the circumference of the unit circle?
Back: 2\pi
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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What is the area of the unit circle?
Back: \pi
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Which real numbers does the point \langle 0, 0 \rangle on the unit circle map to?
Back: N/A. This point is not on the circle itself.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
Which real numbers does the point \langle 1, 0 \rangle on the unit circle map to?
Back: 2\pi k for all k \in \mathbb{Z}.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
Which point on the unit circle does number 2\pi map to?
Back: \langle 1, 0 \rangle
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Which point on the unit circle does number \frac{3\pi}{2} map to?
Back: \langle 0, -1 \rangle
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
Which real numbers does the point \langle 0, -1 \rangle on the unit circle map to?
Back:\frac{3\pi}{2} + 2\pi k for all k \in \mathbb{Z}.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Which real numbers does the point \langle 0, 1 \rangle on the unit circle map to?
Back: \frac{\pi}{2} + 2\pi k for all k \in \mathbb{Z}.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Which point on the unit circle does number \frac{\pi}{2} map to?
Back: \langle 0, 1 \rangle
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
Which point on the unit circle does number \pi map to?
Back: \langle -1, 0 \rangle
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Which real numbers does the point \langle -1, 0 \rangle on the unit circle map to?
Back: \pi + 2\pi k for all k \in \mathbb{Z}.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Which real numbers correspond to the highlighted point on the unit circle?
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Back: 2 \pi k for all k \in \mathbb{Z}.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Which real numbers correspond to the highlighted point on the unit circle?
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Back: \frac{\pi}{2} + 2\pi k for all k \in \mathbb{Z}.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Which real numbers correspond to the highlighted point on the unit circle?
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Back: \pi + 2\pi k for all k \in \mathbb{Z}.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Which real numbers correspond to the highlighted point on the unit circle?
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Back: \frac{3\pi}{2} + 2\pi k for all k \in \mathbb{Z}.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Why does point \langle 1, 0 \rangle on the unit circle coincide with real number 2\pi?
Back: Because the circumference of the unit circle is 2\pi.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
Why does point \langle -1, 0 \rangle on the unit circle coincide with real number \pi?
Back: Because half the circumference of the unit circle is \pi.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
What is the "periodicity" of the unit circle?
Back: 2 \pi
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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%%ANKI Basic What property of the unit circle does its periodicity correspond to? Back: Its circumference. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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What arc describes the portion of a unit circle found in the first quadrant?
Back: \left(0, \frac{\pi}{2}\right)
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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What arc describes the portion of a unit circle found in the third quadrant?
Back: \left(\pi, \frac{3\pi}{2}\right)
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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What arc describes the portion of a unit circle found in the fourth quadrant?
Back: \left(\frac{3\pi}{2}, 2\pi\right)
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Basic
What arc describes the portion of a unit circle found in the second quadrant?
Back: \left(\frac{\pi}{2}, \pi\right)
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Suppose interval [a, b] is mapped to the unit circle. What is the point corresponding to a called?
Back: The initial point.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Suppose interval [a, b] is mapped to the unit circle. What is the point corresponding to b called?
Back: The terminal point.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Map \left[0, \frac{\pi}{2}\right] onto the unit circle. What is the initial point of this arc?
Back: \langle 1, 0 \rangle
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Map \left[0, \frac{\pi}{2}\right] onto the unit circle. What is the terminal point of this arc?
Back: \langle 0, 1 \rangle
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Map \left(0, \frac{\pi}{2}\right) onto the unit circle. What is the initial point of this arc?
Back: N/A. There is no initial point.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Map \left(0, \frac{\pi}{2}\right) onto the unit circle. What is the terminal point of this arc?
Back: N/A. There is no terminal point.
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Map \left[-\pi, -\frac{\pi}{2}\right] onto the unit circle. What is the initial point of this arc?
Back: \langle -1, 0 \rangle
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
Map \left[-\pi, -\frac{\pi}{2}\right] onto the unit circle. What is the terminal point of this arc?
Back: \langle 0, -1 \rangle
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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%%ANKI Cloze Moving in the {positive} direction of the real number line corresponds to moving {counterclockwise} on the unit circle. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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%%ANKI Cloze Moving in the {negative} direction of the real number line corresponds to moving {clockwise} on the unit circle. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Bibliography
- Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.