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title TARGET DECK FILE TAGS tags
Unit Circle Obsidian::STEM trigonometry
trigonometry
unit-circle

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.

%%ANKI 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.

END%%

%%ANKI 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.

END%%

%%ANKI Basic What is the radius of the unit circle? Back: 1 Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.

END%%

%%ANKI Basic What is the diameter of the unit circle? Back: 2 Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.

END%%

%%ANKI Basic What is the circumference of the unit circle? Back: 2\pi Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.

END%%

%%ANKI Basic What is the area of the unit circle? Back: \pi Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.

END%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI Basic Which real numbers correspond to the highlighted point on the unit circle? !unit-circle-1-0.png Back: 2 \pi k for all k \in \mathbb{Z}. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.

END%%

%%ANKI Basic Which real numbers correspond to the highlighted point on the unit circle? !unit-circle-0-1.png Back: \frac{\pi}{2} + 2\pi k for all k \in \mathbb{Z}. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.

END%%

%%ANKI Basic Which real numbers correspond to the highlighted point on the unit circle? !unit-circle-n1-0.png Back: \pi + 2\pi k for all k \in \mathbb{Z}. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.

END%%

%%ANKI Basic Which real numbers correspond to the highlighted point on the unit circle? !unit-circle-0-n1.png Back: \frac{3\pi}{2} + 2\pi k for all k \in \mathbb{Z}. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.

END%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI Basic What interval maps to 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%%

%%ANKI Basic What interval maps to 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.

END%%

%%ANKI Basic What interval maps to 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.

END%%

%%ANKI Basic What interval maps to 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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%%

%%ANKI 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.

END%%

%%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.

END%%

%%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.

END%%

Bibliography

  • Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.