Grade 11 College Math - Primary Trigonometry, Sine Law, and Cosine Law

Vocabulary practice flashcards covering primary trigonometric ratios, angles of elevation and depression, the Sine Law, and the Cosine Law from Grade 11 College Math notes.

Pythagorean Theorem

A mathematical formula for right triangles given by $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.

Hypotenuse

The longest side of a right triangle, located directly across from the right ($90^\circ$) angle.

Legs

The two sides of a right triangle that intersect to form the right ($90^\circ$) angle.

Opposite Side

The side of a right triangle situated directly across from a specified reference angle.

Adjacent Side

The side of a right triangle that forms one side of a specified reference angle along with the hypotenuse, located next to the reference angle.

Primary Trigonometric Ratios

The ratios comparing the lengths of two sides in a right triangle relative to a reference angle: sine ($\sin(\theta)$), cosine ($\cos(\theta)$), and tangent ($\tan(\theta)$).

Sine Ratio

The primary trigonometric ratio defined as the opposite side length divided by the hypotenuse length: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Cosine Ratio

The primary trigonometric ratio defined as the adjacent side length divided by the hypotenuse length: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.

Tangent Ratio

The primary trigonometric ratio defined as the opposite side length divided by the adjacent side length: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

SOH CAH TOA

A mnemonic device used to remember the primary trigonometric ratios: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent.

Angle of Elevation

The angle formed between the horizontal line of sight and the observer's line of sight when looking UP at an object above eye level.

Angle of Depression

The angle formed between the horizontal line of sight and the observer's line of sight when looking DOWN at an object below eye level.

Acute Triangle

A triangle in which all three interior angles are acute, meaning each angle measures less than $90^\circ$.

Sine Law

A trigonometric rule stating that in any acute triangle, the ratio of each side length to the sine of its opposite angle is equal: $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$.

Cosine Law

A trigonometric relationship stating that $a^2 = b^2 + c^2 - 2 \cdot b \cdot c \cdot \cos(A)$, used when given two sides and a contained angle or all three sides.

Contained Angle

An acute angle located directly between two known side lengths in a triangle.

Solving a Triangle

The process of calculating the values of all three side lengths and all three interior angles of a triangle.