Unit 1: How Do They Measure Up? - Trigonometry and Trigonometric Functions

Vocabulary flashcards covering key terms and definitions from Unit 1: Right-Angle Trigonometry, the Law of Sines and Cosines, applications of bearings and angles of elevation/depression, and modeling periodic phenomena with trigonometric functions.

Right-Angle Trigonometry

The branch of mathematics exploring the relationships between side lengths and acute angles in triangles containing a $90^\circ$ angle.

Trigonometric Ratio

A ratio comparing the lengths of two sides of a right-angled triangle relative to one of its acute angles.

Sine Ratio

In a right-angled triangle, the ratio comparing the length of the opposite side to the hypotenuse: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Cosine Ratio

In a right-angled triangle, the ratio comparing the length of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Tangent Ratio

In a right-angled triangle, the ratio comparing the length of the opposite side to the adjacent side: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Angle of Elevation

The angle formed between a horizontal line of sight and an observer's line of sight directed upward toward an object.

Angle of Depression

The angle formed between a horizontal line of sight and an observer's line of sight directed downward toward an object.

Three-Figure Bearing

A navigational angle specifying direction measured clockwise from due north ($000^\circ$), conventionally written using three digits (such as $037^\circ$ or $060^\circ$).

Special Triangles

Right-angled triangles with angle measures of $30^\circ$-$60^\circ$-$90^\circ$ and $45^\circ$-$45^\circ$-$90^\circ$, which feature known exact geometric side-length relationships.