Algebra and Trigonometry Vocabulary

Vocabulary flashcards covering key definitions, formulas, angle classifications, progressions, logarithms, and triangle laws from Day 5 Mathematics lecture notes.

Arithmetic Progression

A series of numbers having a common difference.

Common Difference

The constant difference $d = a_2 - a_1$ between consecutive terms in an arithmetic progression, which is positive for an increasing series and negative for a decreasing series.

Arithmetic Mean

The number or quantity between two terms of an arithmetic series, calculated for two terms $a$ and $b$ as $\frac{a + b}{2}$.

Geometric Progression

A series of numbers having a common ratio.

Common Ratio

The constant ratio $r = \frac{a_2}{a_1}$ between consecutive terms in a geometric progression.

Geometric Mean

The number or quantity between two terms of a geometric series, calculated for two terms $a$ and $b$ as $\sqrt{ab}$.

Sum of Infinite Geometric Series

The sum $S = \frac{a}{1 - r}$ of an infinite geometric progression with first term $a$ and common ratio $r$, provided $r \neq 1$.

Harmonic Progression

A series of numbers whose reciprocals form an arithmetic progression.

Acute Angle

An angle less than $90^\circ$.

Obtuse Angle

An angle more than $90^\circ$ but less than $180^\circ$.

Reflex Angle

An angle more than $180^\circ$ but less than $360^\circ$.

Complementary Angles

Angles whose sum is $90^\circ$.

Supplementary Angles

Angles whose sum is $180^\circ$.

Angle Measurement Units

Angular measurement equivalencies where $1\text{ degree} = 60\,\text{min}$, $1\text{ min} = 60\,\text{sec}$, $90\text{ deg} = 100\text{ grad}$, $\pi\,\text{rad} = 180\text{ deg}$, and $1\text{ rev} = 2\pi\,\text{rad} = 360\text{ deg} = 400\text{ grad} = 6400\text{ mills}$.

Pythagorean Theorem

The theorem given by $c^2 = a^2 + b^2$, where $a$ is the opposite side, $b$ is the adjacent side, and $c$ is the hypotenuse of a right triangle.

Angle of Elevation

The angle above the horizontal plane of the observer.

Angle of Depression

The angle below the horizontal plane of the observer.

Logarithm

A power to which a number (the base) must be raised in order to get some other number.

Exponential Growth and Decay

Models that usually take the form $x = x_0 e^{kt}$, where $x$ is the amount at any period, $x_0$ is the original amount, $k$ is a constant, and $t$ is time.

Half-Life

The time at which an exponentially decaying quantity reaches $x = \frac{x_0}{2}$.

Sine Law

A trigonometric law for oblique triangles stating $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$.

Cosine Law

A trigonometric law for oblique triangles given by equations such as $c^2 = a^2 + b^2 - 2ab \cos(C)$.

Bearing and Directions

Directional orientations including Northwest ($45^\circ$ between N and W), Northeast ($45^\circ$ between N and E), Southwest ($45^\circ$ between S and W), and Southeast ($45^\circ$ between S and E).