Trigonometry Unit Overview

Trigonometry

Study of relationships between angles and sides of triangles

Right Triangle

Triangle with a 90-degree angle

Radians

Unit of measuring angles; 2π radians = 360 degrees

Unit Circle

Circle with radius 1 used to define trigonometric functions

Sine

Ratio of the length of the side opposite an angle to the hypotenuse

Cosine

Ratio of the length of the side adjacent to an angle to the hypotenuse

Tangent

Ratio of the length of the side opposite an angle to the side adjacent

Cosecant

Reciprocal of the sine function

Secant

Reciprocal of the cosine function

Cotangent

Reciprocal of the tangent function

Special Right Triangles

Triangles with specific angle measures (30-60-90, 45-45-90)

Trigonometric Ratio

Ratio of two sides in a right triangle

Angle of Elevation

Angle between the line of sight and horizontal line

Altitude

Perpendicular segment from a vertex to the opposite side

Hypotenuse

Longest side of a right triangle, opposite the right angle

Angle of Depression

Angle below the horizontal line of sight

Perimeter

Sum of all sides of a polygon

Diagonal

Straight line connecting two non-adjacent vertices in a polygon

Rhombus

Quadrilateral with all sides of equal length

Acute Angle

Angle less than 90 degrees

Segment

Part of a line between two points

Vertical Angle

Pair of non-adjacent angles formed by two intersecting lines

Angle

Formed by rotating a ray around its initial point

Initial Side

Starting position of a ray

Terminal Side

Ray's position after rotation

Vertex

Initial point of rays in an angle

Standard Position

Vertex at origin, initial side on positive x-axis

Quadrantal Angle

Angle with terminal side on x- or y-axis

Positive Angles

Rotate counterclockwise

Negative Angles

Rotate clockwise

Degrees

360° in a full revolution

Co-Terminal Angles

Have same initial and terminal sides

Reference Angles

Acute angle formed with x-axis

Supplementary Angles

Sum to 180°

Reference Angle

Angle between terminal side and x-axis

Co-terminal Angle

Angles that share the same terminal side

Quadrant

Region where the angle lies in a coordinate plane

Complement

Sum of angle and its complement is 90 degrees

Supplement

Sum of angle and its supplement is 180 degrees

Trigonometric Functions

Functions like sin, cos, tan, csc, sec, cot