More basic trigonometry notes.

2025-01-19 22:13:56 -07:00 · 2025-01-19 22:13:56 -07:00 · 893334a81d
parent cbeb26fbde
commit 893334a81d
6 changed files with 464 additions and 110 deletions
--- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
+++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
@ -257,7 +257,8 @@
    "function-general.png",
    "function-kernel.png",
    "triangular-gnomon.png",
-    "pascals-triangle.png"
+    "pascals-triangle.png",
+    "example-arc.png"
  ],
  "File Hashes": {
    "algorithms/index.md": "3ac071354e55242919cc574eb43de6f8",
@ -1464,12 +1465,13 @@
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-    "geometry/circle.md": "751a5aada6521281f1d8edb463572943",
+    "trigonometry/index.md": "06c82d1cf3789cc8cefd37e6b64fdc4a",
+    "geometry/circle.md": "9469e5512a6a92a962985eab99d00606",
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+    "trigonometry/unit-circle.md": "4a8fb4b5ac1bc2b645f18b0b8079897c"
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  "fields_dict": {
    "Basic": [
--- a/notes/_journal/2025-01-19.md
+++ b/notes/_journal/2025-01-19.md
@ -9,3 +9,4 @@ title: "2025-01-19"
 - [ ] Korean (Read 1 Story)

 * More notes on relocation entries.
+* More notes on basic trigonometry.
--- a/notes/geometry/circle.md
+++ b/notes/geometry/circle.md
@ -13,7 +13,7 @@ A **circle** is a shape consisting of all points in a plane at a given distance

 On the [[cartesian|Cartesian coordinate system]], the equation of a circle with radius $r$ and center $\langle h, k \rangle$ is $$(x - h)^2 + (y - k)^2 = r^2.$$

-Such a circle has circumference $2\pi r$ and [[area]] $\pi r^2$.
+Such a circle has circumference $2\pi r$ and [[area]] $\pi r^2$. A continuous segment along the circumference of a circle is called an **arc**.

 %%ANKI
 Basic
@ -195,6 +195,15 @@ Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.
 <!--ID: 1737168379578-->
 END%%

+%%ANKI
+Basic
+What term is used to describe a continuous portion of a circle?
+Back: An arc.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737347029852-->
+END%%
+
 ## Bibliography

 * “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+* Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
--- a/notes/trigonometry/images/example-arc.png
+++ b/notes/trigonometry/images/example-arc.png
--- a/notes/trigonometry/index.md
+++ b/notes/trigonometry/index.md
@ -8,7 +8,9 @@ tags:

 ## Overview

-Trigonometry was originally derived from a Greek word meaning "triangle measuring". It has generalized to studying periodicity.
+Trigonometry was originally derived from a Greek word meaning "triangle measuring". It has since been generalized to refer to the study of periodicity.
+
+If the real number $t$ is the directed length of an arc (either positive or negative) measured on the [[unit-circle|unit circle]] $x^2 + y^2 = 1$ (with counterclockwise as the positive direction) with initial point $\langle 1, 0 \rangle$ and terminal point $\langle x, y \rangle$, then the **cosine** of $t$, denoted $\cos(t)$, and **sine** of $t$, denoted $\sin(t)$, are defined to be $$\cos(t) = x \quad\text{and}\quad \sin(t) = y.$$

 %%ANKI
 Basic
@ -18,196 +20,220 @@ Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
 <!--ID: 1737167693405-->
 END%%

-## Unit Circle
-
-On the [[cartesian|Cartesian coordinate system]], the **unit circle** is the [[circle]] with center at the origin and radius $1$.
-
 %%ANKI
 Basic
-On the Cartesian coordinate system, what is the unit circle?
-Back: The circle with center at the origin and radius $1$.
+What are the two most fundamental trigonometric functions?
+Back: $\sin$ and $\cos$.
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737167693410-->
+<!--ID: 1737349513249-->
+END%%
+
+%%ANKI
+Cloze
+The {sine} of $t$ is denoted as {$\sin(t)$}.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349513250-->
+END%%
+
+%%ANKI
+Cloze
+The {cosine} of $t$ is denoted as {$\cos(t)$}.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349513251-->
 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.
+Map $[0, t]$ to the unit circle. Geometrically, what does $\cos(t)$ correspond to?
+Back: The $x$-coordinate of the arc's terminal point.
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737167693413-->
+<!--ID: 1737349513252-->
 END%%

 %%ANKI
 Basic
-What is the radius of the unit circle?
-Back: $1$
+Map $[0, t]$ to the unit circle. Geometrically, what does $\sin(t)$ correspond to?
+Back: The $y$-coordinate of the arc's terminal point.
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737167693416-->
+<!--ID: 1737349513253-->
+END%%
+
+%%ANKI
+Cloze
+The {1:$x$}-coordinate is to {2:$\cos$} whereas the {2:$y$}-coordinate is to {1:$\sin$}.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349513254-->
 END%%

 %%ANKI
 Basic
-What is the diameter of the unit circle?
-Back: $2$
-Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737167693419-->
-END%%
-
-%%ANKI
-Basic
-What is the circumference of the unit circle?
-Back: $2\pi$
-Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737167693428-->
-END%%
-
-%%ANKI
-Basic
-What is the area of the unit circle?
-Back: $\pi$
-Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737167693435-->
-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.
-<!--ID: 1737168795237-->
-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.
-<!--ID: 1737168795241-->
-END%%
-
-%%ANKI
-Basic
-Which point on the unit circle does number $2\pi$ map to?
+Suppose an arc on the unit circle has terminal point $\langle \cos(t), \sin(t) \rangle$. What was its initial point?
 Back: $\langle 1, 0 \rangle$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737168795265-->
+<!--ID: 1737349513255-->
 END%%

 %%ANKI
 Basic
-Which point on the unit circle does number $\frac{3\pi}{2}$ map to?
-Back: $\langle 0, -1 \rangle$
+What geometric aspect of the unit circle corresponds to the input of the cosine function?
+Back: Arc length.
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737168795244-->
+<!--ID: 1737349513257-->
 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 $k \in \mathbb{Z}$.
+What geometric aspect of the unit circle corresponds to the output of the cosine function?
+Back: The $x$-coordinate of an arc's terminal point.
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737168795269-->
+<!--ID: 1737349513258-->
 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 $k \in \mathbb{Z}$.
+What geometric aspect of the unit circle corresponds to the input of sine?
+Back: Arc length.
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737168795248-->
+<!--ID: 1737349513259-->
 END%%

 %%ANKI
 Basic
-Which point on the unit circle does number $\frac{\pi}{2}$ map to?
-Back: $\langle 0, 1 \rangle$
+What geometric aspect of the unit circle corresponds to the output of the sine function?
+Back: The $y$-coordinate of an arc's terminal point.
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737168795261-->
+<!--ID: 1737349513261-->
 END%%

 %%ANKI
 Basic
-Which point on the unit circle does number $\pi$ map to?
-Back: $\langle -1, 0 \rangle$
+Consider the following arc with length $t$ on the unit circle. What is the terminal point's $x$-coordinate?
+![[example-arc.png]]
+Back: $\cos(t)$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737168795252-->
+<!--ID: 1737349513260-->
 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 $k \in \mathbb{Z}$.
+Consider the following arc with length $t$ on the unit circle. What is the terminal point's $y$-coordinate?
+![[example-arc.png]]
+Back: $\sin(t)$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737168795256-->
+<!--ID: 1737349513256-->
 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 $k \in \mathbb{Z}$.
+Consider the following arc with length $t$ on the unit circle. With maximum specificity, what is its terminal point?
+![[example-arc.png]]
+Back: $\langle \cos(t), \sin(t) \rangle$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737169243685-->
+<!--ID: 1737349513262-->
 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 $k \in \mathbb{Z}$.
+What does $\cos(0)$ evaluate to?
+Back: $1$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737169243690-->
+<!--ID: 1737349971441-->
 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 $k \in \mathbb{Z}$.
+What does $\cos\left(\frac{\pi}{2}\right)$ evaluate to?
+Back: $0$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737169243692-->
+<!--ID: 1737349971443-->
 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 $k \in \mathbb{Z}$.
+What does $\cos\left(-\frac{\pi}{2}\right)$ evaluate to?
+Back: $0$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737169243695-->
+<!--ID: 1737349971445-->
 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 $2\pi$.
+What does $\cos\left(\pi\right)$ evaluate to?
+Back: $-1$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737169683142-->
+<!--ID: 1737349971446-->
 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 $\pi$.
+What does $\sin(2\pi)$ evaluate to?
+Back: $0$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737169683151-->
+<!--ID: 1737349971447-->
 END%%

 %%ANKI
 Basic
-What is the "periodicity" of the unit circle?
-Back: $2 \pi$
+What does $\sin\left(\frac{\pi}{2}\right)$ evaluate to?
+Back: $1$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737230158153-->
+<!--ID: 1737349971449-->
 END%%

 %%ANKI
 Basic
-What property of the unit circle does its periodicity correspond to?
-Back: Its circumference.
+What does $\sin\left(-\frac{\pi}{2}\right)$ evaluate to?
+Back: $-1$
 Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
-<!--ID: 1737230158163-->
+<!--ID: 1737349971450-->
+END%%
+
+%%ANKI
+Basic
+What does $\sin\left(\pi\right)$ evaluate to?
+Back: $0$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349971451-->
+END%%
+
+%%ANKI
+Basic
+Why are $\sin$ and $\cos$ called circular functions?
+Back: Their values are determined by coordinates of points on the unit circle.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349971452-->
+END%%
+
+%%ANKI
+Basic
+What is the domain of $\cos$?
+Back: $\mathbb{R}$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349971453-->
+END%%
+
+%%ANKI
+Basic
+What is the range of $\cos$?
+Back: $[-1, 1]$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349971454-->
+END%%
+
+%%ANKI
+Basic
+What is the domain of $\sin$?
+Back: $\mathbb{R}$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349971455-->
+END%%
+
+%%ANKI
+Basic
+What is the range of $\sin$?
+Back: $[-1, 1]$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737349971456-->
 END%%

 ## Bibliography
--- a/notes/trigonometry/unit-circle.md
+++ b/notes/trigonometry/unit-circle.md
@ -0,0 +1,316 @@
+---
+title: Unit Circle
+TARGET DECK: Obsidian::STEM
+FILE TAGS: trigonometry
+tags:
+  - trigonometry
+  - unit-circle
+---
+
+## Overview
+
+On the [[cartesian|Cartesian coordinate system]], the **unit circle** is the [[circle]] with center at the origin and radius $1$.
+
+Suppose [[intervals|closed interval]] $[a, b]$ 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.
+<!--ID: 1737167693410-->
+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.
+<!--ID: 1737167693413-->
+END%%
+
+%%ANKI
+Basic
+What is the radius of the unit circle?
+Back: $1$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693416-->
+END%%
+
+%%ANKI
+Basic
+What is the diameter of the unit circle?
+Back: $2$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693419-->
+END%%
+
+%%ANKI
+Basic
+What is the circumference of the unit circle?
+Back: $2\pi$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693428-->
+END%%
+
+%%ANKI
+Basic
+What is the area of the unit circle?
+Back: $\pi$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693435-->
+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.
+<!--ID: 1737168795237-->
+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.
+<!--ID: 1737168795241-->
+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.
+<!--ID: 1737168795265-->
+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.
+<!--ID: 1737168795244-->
+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.
+<!--ID: 1737168795269-->
+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.
+<!--ID: 1737168795248-->
+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.
+<!--ID: 1737168795261-->
+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.
+<!--ID: 1737168795252-->
+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.
+<!--ID: 1737168795256-->
+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.
+<!--ID: 1737169243685-->
+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.
+<!--ID: 1737169243690-->
+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.
+<!--ID: 1737169243692-->
+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.
+<!--ID: 1737169243695-->
+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.
+<!--ID: 1737169683142-->
+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.
+<!--ID: 1737169683151-->
+END%%
+
+%%ANKI
+Basic
+What is the "periodicity" of the unit circle?
+Back: $2 \pi$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737230158153-->
+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.
+<!--ID: 1737230158163-->
+END%%
+
+%%ANKI
+Basic
+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.
+<!--ID: 1737347029839-->
+END%%
+
+%%ANKI
+Basic
+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.
+<!--ID: 1737347029841-->
+END%%
+
+%%ANKI
+Basic
+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.
+<!--ID: 1737347029843-->
+END%%
+
+%%ANKI
+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.
+<!--ID: 1737347029844-->
+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.
+<!--ID: 1737347029845-->
+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.
+<!--ID: 1737347029847-->
+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.
+<!--ID: 1737347029848-->
+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.
+<!--ID: 1737347029849-->
+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.
+<!--ID: 1737347029850-->
+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.
+<!--ID: 1737347029851-->
+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.
+<!--ID: 1737349513245-->
+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.
+<!--ID: 1737349513248-->
+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.
+<!--ID: 1737347197473-->
+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.
+<!--ID: 1737347197477-->
+END%%
+
+## Bibliography
+
+* Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.