Trigonometry and Conics Flashcards

Vocabulary flashcards covering key terms from Trigonometry, Conics, Polar Equations, and Parametric Functions.

Angles

Measure of the space formed by two lines diverging from a common point (vertex).

Radians

A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius.

Trigonometric Ratios

Ratios relating the sides of a right triangle to its angles (sine, cosine, tangent, etc.).

Unit Circle

A circle with a radius of 1, often used to define trigonometric functions.

Sine

A trigonometric function that, for an acute angle, is the ratio between the leg opposite to that angle when considered as part of a right triangle and the longest side of the triangle (the hypotenuse).

Cosine

A trigonometric function that, for an acute angle, is the ratio between the leg adjacent to that angle when considered as part of a right triangle and the longest side of the triangle (the hypotenuse).

Tangent

A trigonometric function that, for an acute angle, is the ratio between the leg opposite to that angle when considered as part of a right triangle and the leg adjacent to that angle..

Cotangent

A trigonometric function that, for an acute angle, is the ratio between the leg adjacent to that angle when considered as part of a right triangle and the leg opposite to that angle..

Secant

A trigonometric function that, for an acute angle, is the ratio between the hypotenuse of the right triangle and the leg adjacent to that angle.

Cosecant

A trigonometric function that, for an acute angle, is the ratio between the hypotenuse of the right triangle and the leg opposite to that angle.

Amplitude

The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.

Period

The interval required for one complete oscillation or cycle.

Inverse Trigonometric Functions

The inverse functions of the trigonometric functions (arcsin, arccos, arctan, etc.).

Pythagorean Identities

Trigonometric identities based on the Pythagorean theorem.

Sum and Difference Identities

Identities expressing trigonometric functions of sums and differences of angles.

Half Angle Identities

Identities expressing trigonometric functions of half angles.

Double Angle Identities

Identities expressing trigonometric functions of double angles.

Law of Sines

A relationship between the sides and angles of non-right (oblique) triangles.

Law of Cosines

A relationship between the sides and angles of non-right (oblique) triangles, generalizing the Pythagorean theorem.

Vectors

Quantities that have both magnitude and direction.

Dot Product

An algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.

Parabola

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side.

Hyperbola

A symmetrical open curve formed by the intersection of a cone with a plane that intersects the base.

Ellipse

A regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant.

Double-Napped Cone

A cone with two identical halves, or nappes, extending infinitely in opposite directions from the vertex.

Center

The central point inside a circle or other symmetrical figure.

Asymptotes

A line that a curve approaches arbitrarily closely.

Locus

A set of points whose location satisfies or is determined by one or more specified conditions.

Conic

A curve obtained as the intersection of the surface of a cone with a plane.

Focus/Foci

A point at which rays or waves meet after reflection or refraction, or the point from which diverging rays or waves appear to proceed.

Transverse Axis

The axis of symmetry of a hyperbola that passes through the vertices.

Conjugate Axis

The axis of a hyperbola that is perpendicular to the transverse axis and passes through the center.

Major Axis

The longest diameter of an ellipse.

Co-Vertices

The endpoints of the minor axis of an ellipse.

Minor Axis

The shortest diameter of an ellipse.

Axis of Symmetry

A line that divides a figure into two congruent halves.

Vertex/Vertices

A point where two or more curves, lines, or edges meet.

Directrix

A line used to define a conic section, especially a parabola.

Polar Coordinate Plane

A two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

Polar to Rectangular Coordinate conversions

Converting from polar coordinates (r, θ) to rectangular coordinates (x, y) using x = rcosθ and y = rsinθ.

Cardioid

A heart-shaped polar curve.

Lemniscate

A figure-eight-shaped polar curve.

Limaçon

A polar curve resembling a snail or a dimpled circle.

Rose

A polar curve with petal-like loops.

Parametric Equations

A set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters.