Trigonometry Terms and Definitions
Trigonometry
Trigonometry
Definition:
The branch of mathematics that examines the relationships between the angles and sides of triangles, primarily through trigonometric functions like sine, cosine, and tangent.
Plane Angle
Definition:
A geometric figure formed by two rays sharing a common endpoint, measured as the rotation from one ray (the initial side) to the other (the terminal side).
Vertex
Definition:
The common endpoint of two rays or line segments that define an angle or form a corner in a geometric figure.
Initial Side
Definition:
The fixed starting ray of an angle from which rotation begins to define the angle.
Terminal Side
Definition:
The ray that results after rotating the initial side to form an angle.
Positive Angle
Definition:
An angle measured counterclockwise from the initial side to the terminal side.
Negative Angle
Definition:
An angle measured clockwise from the initial side to the terminal side.
Degree
Definition:
A unit of angular measure where one degree equals 1/360 of a complete circle.
Minute
Definition:
A subunit of a degree, where one minute equals 1/60 of a degree.
Second
Definition:
A subunit of a minute, where one second equals 1/60 of a minute or 1/3600 of a degree.
Radian
Definition:
A measure of an angle based on the arc length of a circle, defined as the angle subtended by an arc equal in length to the radius of the circle.
Arc Length
Definition:
The distance along the curve of a circle, determined by the product of the circle's radius and the central angle in radians.
Central Angle
Definition:
An angle formed by two radii of a circle, with its vertex at the center of the circle.
Unit Circle
Definition:
A circle with a radius of one unit, used in trigonometry to define and evaluate trigonometric functions.
Sector
Definition:
A portion of a circle bounded by two radii and the arc between them.
Area Of A Sector
Definition:
The area of a slice of a circle, calculated as half the product of the radius squared and the central angle in radians.
Angular Velocity
Definition:
The rate of change of an angle over time, expressed in radians per unit time.
Linear Velocity
Definition:
The rate at which a point moves along the circumference of a circular path, calculated as the product of the radius and the angular velocity.
Directed Line
Definition:
A line with an assigned positive and negative direction, used to measure distances with sign.
Rectangular Coordinate System
Definition:
A two-dimensional plane defined by perpendicular horizontal and vertical axes intersecting at an origin, used to locate points using ordered pairs of numbers.
Abscissa
Definition:
The horizontal coordinate of a point in a rectangular coordinate system, representing its distance from the vertical axis.
Ordinate
Definition:
The vertical coordinate of a point in a rectangular coordinate system, representing its distance from the horizontal axis.
Quadrant
Definition:
One of the four regions of a rectangular coordinate system, divided by the x-axis and y-axis.
Radius Vector
Definition:
The straight-line distance from the origin to a point in a rectangular coordinate system.
Angle In Standard Position
Definition:
An angle with its vertex at the origin of a coordinate system and its initial side along the positive x-axis.
Coterminal Angles
Definition:
Angles that share the same terminal side when placed in standard position, differing by integer multiples of 360°.
Quadrantal Angles
Definition:
Angles whose terminal sides lie along the axes in a coordinate system, such as 0°, 90°, 180°, and 270°.
Reciprocal Trigonometric Functions
Definition:
Functions defined as the reciprocals of the primary trigonometric functions, including cosecant (csc), secant (sec), and cotangent (cot).
Unit Circle
Definition:
A circle with a radius of one, centered at the origin in a coordinate plane, used to define trigonometric functions.
Circular Functions
Definition:
Functions like sine and cosine defined as the coordinates of a point on the unit circle, applicable to all real numbers.
Undefined Trigonometric Functions
Definition:
Trigonometric functions that do not have a value for specific angles due to division by zero.
Arc Length On Unit Circle
Definition:
The length of an arc on the unit circle, numerically equal to the measure of the angle in radians.
Wrapping Function
Definition:
A function that maps real numbers to points on the unit circle by associating arc lengths with coordinates (cos(s), sin(s)).
Signs Of Trigonometric Functions
Definition:
The positivity or negativity of trigonometric functions in different quadrants based on the signs of x and y coordinates.
Circular Angle Measures
Definition:
Angles measured in radians, where the arc length on the unit circle equals the angle in radians.
Domain Of Trigonometric Functions
Definition:
The set of input values (angles) for which trigonometric functions are defined.
Evaluation Of Trigonometric Functions
Definition:
Calculating specific trigonometric values for given angles using known properties, quadrants, or the unit circle.
Periodicity Of Trigonometric Functions
Definition:
A property of trigonometric functions where their values repeat at regular intervals, such as 2π for sine and cosine.
Even Function
Definition:
A function f(x) that satisfies f(−x) = f(x), with the graph symmetric about the y-axis; examples include cosine and secant.
Odd Function
Definition:
A function f(x) that satisfies f(−x)=−f(x), with the graph symmetric about the origin; examples include sine and tangent.