5.7 KiB
| title | TARGET DECK | FILE TAGS | tags | |
|---|---|---|---|---|
| Trigonometry | Obsidian::STEM | trigonometry |
|
Overview
Trigonometry was originally derived from a Greek word meaning "triangle measuring". It has generalized to studying periodicity.
%%ANKI Basic Trigonometry was originally the study of what geometric shape? Back: Triangles. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
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Unit Circle
On the cartesian, the unit circle is the circle with center at the origin and radius 1.
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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.
END%%
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Basic
What is the diameter of the unit circle?
Back: 2
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
What is the circumference of the unit circle?
Back: 2\pi
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
What is the area of the unit circle?
Back: \pi
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
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Basic
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.
END%%
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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.
END%%
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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.
END%%
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Basic
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.
END%%
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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.
END%%
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Basic
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.
END%%
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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?
!
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?
!
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?
!
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.
END%%
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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.
END%%
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Basic
What is the "periodicity" of the unit circle?
Back: 2 \pi
Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
%%ANKI Basic What property of the unit circle does its periodicity correspond to? Back: Its circumference. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
Bibliography
- Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.