# TRIGONOMETRY GLOSSARY

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Arccos The inverse cosine.
Given the number that represents the cosine of an angle, the arccosine of the number returns the angle whose cosine is the given number.
Arccot The inverse cotangent.
Given the number that represents the cotangent of an angle, the arccotangent of the number returns the angle whose cotangent is the given number.
Arccsc The inverse cosecant.
Given the number that represents the cosecant of an angle, the arccosecant of the number returns the angle whose cosecant is the given number.
Arcsec The inverse secant.
Given the number that represents the secant of an angle, the arcsecant of the number returns the angle whose secant is the given number.
Arcsin The inverse sine.
Given the number that represents the sine of an angle, the arcsine of the number returns the angle whose sine is the given number.
Arctan The inverse tangent.
Given the number that represents the tangent of an angle, the arctangent of the number returns the angle whose tangent is the given number.
Argument of a Vector The angle at which a vector is directed.
ASTC Mnemonic device for remembering which trig functions are positive in the four Cartesian quadrants.
Bearing The direction of a vector can be a heading or a bearing.
Heading implies movement along a compass direction.
Bearing implies a static compass direction.
Beta Beta is the second letter of the Greek alphabet.
Catenary Curve The curve formed by hanging a rope or chain between two posts is a Catenary Curve.
Its math function is that of the hyperbolic cosine function.
Circular Functions Circular Functions are based on the properties of circles, which are plane figures where every point on the circle is equidistant from a center point.
Cofunctions Each of the six basic trigonometric functions have a cofunction.
Their names tell the story: sine and cosine, tangent and cotangent, secant and cosecant are each pairs of cofunctions.
Cosecant One of the six basic trig functions, the Cosecant function is the reciprocal of the sine function, and the cofunction of the secant.
The Cosecant of theta can be expressed as (r/y) for an angle in standard position, or the ratio of hypotenuse over opposite side in a right triangle.
Cosine One of the six basic trig functions, the Cosine is the cofunction of the sine function and the reciprocal of the secant function.
In standard position the Cosine of theta is (x/r).
In a right triangle the cosine of an angle is the ratio of the adjacent side to the hypotenuse.
Cotangent One of the six basic trig function, Cotangent is both the reciprocal function and the cofunction of the tangent function.
For a right triangle, the Cotangent of an angle is the ratio of adjacent side to the opposite.
In standard position for angle theta, the Cotangent can be expressed as (x/y).
DeMoivre's Theorem This theorem allows quick calculations of powers and roots of complex numbers expressed in trigonometric form.
Euler's Formula (Complex) Euler's Formula for complex numbers expresses a complex number in trigonometric form.
Euler's Formula (Polyhedra) V - E + F = 2.
For any polyhedron, the number of vertices minus the number of edges plus the number of faces equals two.
Gamma Gamma is the third letter of the Greek alphabet.
Great Circle Basically, any circle that resides on a sphere is a Great Circle.
Greek Anyone interested in learning mathematics should embrace the Greek alphabet with 24 letters from alpha to omega.
Harmonic A small integral multiple (or divisor) of a waveform is a harmonic.
Heading Quite similar to bearing, Heading is a dynamic direction that implies motion.
Heron's Formula A wonderful little recipe (algorithm) for finding the area of a triangle when sides are known and the altitude is not known, the formula is best expressed with a semiperimeter.
Horizontal Horizontal comes from orientation like the horizon; parallel to the "flat" surface of the earth; perpendicular to vertical.
Hyperbolic Geometry Hyperbolic Geometry is non-Euclidean geometry; within it the Parallel Postulate does not hold.
Hypotenuse The longest side of a right triangle is the Hypotenuse; it is always opposite the 90-degree angle (or right vertex).
Hypothesis In a biconditional statement the hypothesis is followed by a conclusion.
In the scientific method, the hypothesis is the conjecture to be proved or disproved.
i, Square Root of -1 The small-case i is reserved for the square-root of a negative one; the square of i is -1.
Identity As opposed to a conditional statement that is sometimes true, an Identity will always be true.
The multiplicative identity is 1; the additive identity is zero.
If-and-Only-If (Iff) A statement that shows a condition both necessary and sufficient for the assertion.
If-Then Statement The classic biconditional statement is often phrased as an If-Then proposition.
Imaginary Number Imaginary Numbers exist, but we do not call them "real."
Incenter The center of a circle inscribed within a polygon.
For a triangle, it is the point of concurrence of the angle bisectors.
Infinite In common language, not countable in any practical manner.
In math, having no bounds or boundary.
Infinite Series Any series of terms whose progression has an unlimited (limitless) number of terms is an Infinite Series.
Infinitesimal Infinitely small is Infinitesimal, so tiny that it occupies no space.
While in human terms anything really small (a molecule) is Infinitesimal, in math the term means approaching zero in size.
Infinity That without bound; limitless.
Initial Side of an Angle In standard position, the Initial Side of an Angle is the ray along the positive x-axis, from the origin.
Inscribed Angle An angle inside a circle with its vertex on the circle is an Inscribed Angle.
Inscribed Circle This term is the same as Incircle, a circle inscribed within a polygon.
Interior Angle Any angle inside a geometric entity, or between geometric lines, is considered an Interior Angle.
Interval The space or region between two defined values is an Interval.
Invariant Constant.
Not changing.
Static.
That which does not vary.
Inverse Cosecant Given a number, this function returns the angle whose cosecant is the given number.
Inverse Cosine Given a number, this function returns the angle whose cosine is the given number.
Inverse Cotangent Given a number, this function returns the angle whose cotangent is the given number.
Inverse Secant Given a number, this function returns the angle whose secant is the given number.
Inverse Sine Given a number, this function returns the angle whose sine is the given number.
Inverse Tangent Given a number, this function returns the angle whose tangent is the given number.
Inverse Trigonometric Function Given a number, this function returns the angle whose trig function is the given number.
Iota The ninth letter of the Greek alphabet, Iota means a very small amount.
Isosceles Triangle A triangle with two congruent sides.
Kappa The tenth letter of the Greek alphabet is Kappa, popular on college campuses with sororities and fraternities.
Lambda Lambda is the eleventh letter of the Greek alphabet and is used for wavelength in physics.
Law of Cosines The familiar Pythagorean Theorem is a special case of the Law of Cosines.
Law of Sines The ratio of the sine of any angle within any specific triangle and the length of the opposite side is a constant.
Least Upper Bound As the name implies, a function often has a highest value or a limit beyond which it may not realize.
Leg, Triangle Most generally the legs of a triangle refer to the perpendicular sides of a right triangle only.
Linear Pair Two adjacent supplementary angles form a Linear Pair.
Logarithm A Logarithm is a number associated with a power and a base; the function is the inverse of an exponential function.
Magnitude, Powers of Ten Often when we compare the multiplication by various powers of ten we speak of the magnitude of the effect of the multiplication.
Magnitude, Vectors The Magnitude of a vector is the length of the vector.
We may apply a Pythagorean relation to the perpendicular components of the vector to find the length.
Major Axis Certain conic sections have a Major Axis, a line (segment) between vertices.
Median, Triangle A triangle has three Medians, each a line segment from a vertex to the midpoint of the opposite side of the triangle.
Medians are concurrent at the centroid.
Minor Axis A line or line segment specific to certain conic sections.
Minute, Angle For angles, one Minute is one-sixtieth of a degree.
One Minute is equivalent to 1/21600 of a circular rotation.
Moment of Inertia Each shape or body has an associated Moment of Inertia related to mass distribution and the choice of the axis around which the body is rotated.
Multiplicative Inverse Another name for Multiplicative Inverse is reciprocal.
Reciprocals multiply to one.
N-gon When a polynomial has so many sides that we cannot easily remember its name, we just take the number of sides (n) and add "gon" to our characterization, as a 16-sided polygon would be called a "16-gon."
Negative Reciprocal The product of two Negative Reciprocals is -1.
When lines in Cartesian or rectangular coordinates meet at right angles they have Negative Reciprocal slopes, unless they are precisely horizontal and vertical.
Non-collinear Not linear, not aligned, not part of the same line.
Not collinear.
Non-Euclidean A geometry in which the Parallel Postulate does not hold may be termed a Non-Euclidean geometry.
In such a geometry, the shortest distance between two points may not be a straight line.
Nonagon A nine-sided polygon.
Norm The heavy-set guy from the Boston tavern Cheers.
Actually, its either a kind of average or a length.
Normal Usually meaning orthogonal (as to a plane), Normal sometimes means also merely perpendicular.
Normalize We might Normalize data by culling errors.
Or we might Normalize a vector by assigning a unit vector in its direction.
Nth Root Given some integer N and a real value, the Nth Root of the real value is the number that when raised to the N power returns the real value.
Nu Nu is the 13th letter of the Greek alphabet.
Oblique In one sense, at an angle or not perfectly horizontal or vertical.
An Oblique triangle is any triangle that is not a right triangle.
Obtuse In common language Obtuse means obscure and confusing, obfuscatory.
An Obtuse angle measures more than 90 degrees (and less than 180 degrees).
Octant As we have four quadrants in the rectangular plane, we have eight Octants in rectangular space.
In three dimensions the three axes divide space into eight sections, each termed an Octant.
Odd Function An Odd Function adheres to this property: f(-x) = -f(x).
The standard sine function is an odd function.
Omega The last, or 24th, letter of the Greek alphabet is Omega.
Upper-case Omega is used for ohms, a unit of electrical resistance.
Lower-case Omega is used for angular velocity, a speed of rotation.
Ordered Pair Two coordinates are required to label a point in a plane, typically (x, y).
Ordered Triple Three coordinates are required to label a point in space, typically (x, y, z).
Orthocenter The Orthocenter of a triangle is the point of concurrence of the altitudes of the triangle.
Orthogonal Most generally Orthogonal means perpendicular to a plane.
Parametric Equation In a general sense, we have a Parametric Equation when we define something in specific terms of something else.
Period Measured in time, or angle, or even sometimes distance, the Period of a repetitive function is the time (or angle or distance) it takes to complete a cycle.
Periodic Functions that repeat a cycle over and over again are considered Periodic.
Perpendicular At right angles.
Phase Shift This applies to sinusoids moved left or right by a change to the argument (the angle).
Plane An infinite expanse of points in two dimensions.
Point-
Polar Complex Number We may express complex numbers in trigonometric form.
Polar Coordinates In labeling a point in a plane we need two coordinates.
In Polar Coordinates we use a radius and an angle, as (r, theta).
Polar-Rectangular Conversion An algorithm for changing (r, theta) to (x, y).
Polygon A closed plane figure with straight sides.
Polyhedron A geometric solid with faces that are polygons.
Postulate A far-reaching conjecture or sense of reasoning for which an obvious and substantive base appears most reasonable.
Precision The quality of finer measurement or estimation is termed Precision.
Projectile Motion Projectile Motion is a parabolic arc caused by gravity.
Proportional In a (constant) ratio.
Psi The 23rd letter (next-to-last) of the Greek alphabet.
Pythagorean Identities sin²x + cos²x = 1; 1 + tan²x = sec²x; 1 + cot²x = csc²x
Radian A Radian is an angle (measure) that subtends an arc length (on a circle) equal to the radius of the circle.
Radians are just as good as degrees for measuring angles, and sometimes better.
Radian Measure Radian Measure is just as good as degree measure for angles, and sometimes better.
Pi radians are equivalent to 180 degrees.
Radical A root symbol or the root itself is sometimes termed a Radical.
It is the distance from the center of a circle to any point on the circle.
Ratio Sometimes Ratio is meant to state a constant proportion.
More generally, the Ratio of two real values is the quotient of one number divided by the other.
Ray A set of collinear points, a Ray has an endpoint and proceeds infinitely far in a single direction.
Rectangular-Polar Conversion A simple algorithm to change (x, y) into (r, theta).
Reference Angle In standard position, any angle in quadrants II, III, or IV has a Reference Angle equal to the acute angle made with the x-axis.
Regular Polygon A Regular Polygon is both equilateral (all sides congruent) and equiangular (all angles congruent).
Regular Right Prism A Prism with bases of Regular polygons and lateral faces perpendicular to those bases.
Regular Right Pyramid A Pyramid with a Regular polygon for a base and an apex directly above the center of the base.
Revolutions Per Minute Abbreviated "rpm" it conveys the number of complete circular rotations that occur every 60 seconds at some constant rate of revolution.
Rho Lower-case Rho, the 17th letter of the Greek alphabet, is often used for density (mass per unit volume) in physics.
Right Angle An angle of 90 degrees or pi/2 radians.
Perpendicular lines meet at Right Angles.
Right Circular Cone A cone with a circular base and an apex directly above the center of the base.
Right Circular Cylinder A circular cylinder with sides orthogonal to parallel bases.
Right Cone Any Cone, circular or otherwise, with its apex directly above the center of the base.
Right Cylinder Any Cylinder, circular or otherwise, with lateral sides orthogonal to the bases.
Right Prism A Prism with lateral sides orthogonal to the bases.
Right Pyramid A Pyramid with its apex directly above the center of the base.
Right Regular Prism A Prism with bases of Regular polygons and lateral faces perpendicular to the bases.
Right Regular Pyramid A Pyramid with a Regular polygon for a base and an apex directly above the center of the base.
Right Square Parallelepiped Cube.
Right Square Prism A cube, or a shoebox if the ends of the shoebox are square.
Right Triangle A triangle with a right angle.
Rotation Movement in a circulation or circular fashion, often around a point or an axis, is termed Rotation.
SAA Congruence Side-Angle-Angle Congruence establishes two congruent triangles.
SAS Congruence Side-Angle-Side Congruence establishes Congruence between two triangles.
Scalene A triangle is considered Scalene if no two sides have the same length.
Secant The term applies to either a line containing the chord of a circle (or some other line segment between points on a function), or one of the six basic functions in trigonometry, the cofunction of the cosecant and the reciprocal of the cosine.
Second, Degree While "second degree" applies to a polynomial, a single Second with respect to Degree measure is one-sixtieth of one minute, or one sixtieth of one sixtieth of one degree, or 1/1,296,000 of a revolution.
Second, Time One sixtieth of a minute, or 1/3600 of an hour, is one Second of Time.
Sector A piece of a circle bounded by a central angle.
Similar Geometrically, figures of like shape and proportions are said to be Similar.
Similarity Literally the quality of being Similar, which is to have the same shape and proportions, but not necessarily of the same size.
Simple Harmonic Motion Periodic Motion with constant length of cycle time (a fixed period) is termed Simple Harmonic Motion.
Sine One of the six basic trig functions, in a right triangle the Sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.
Sinusoid A sine wave is called a Sinusoid; a cosine graph is also a Sinusoid.
Skew Lines neither intersecting nor parallel (non-coplanar lines) are termed Skew lines.
Slope A number associated with a line graphed in a plane, Slope is the ratio of rise over run, an indication of the steepness of the line.
We may write a line as y = mx + b and use the value of m for Slope.
Also stands for "some old hippie caught another hippie tripping on acid."
Solution Too often in math class, "the answer." More directly, a Solution is a value (or set of values) that makes a mathematical statement true.
Sphere A three-dimensional figure comprised of points equidistant from a center point; a Sphere has a fixed radius.
Spherical Geometry Unlike plane Geometry, Spherical Geometry is not based on the parallel postulate.
Many of our accepted geometric theorems, principles, and tenets (from plane Geometry) simply do not hold in Spherical Geometry.
Spherical Trigonometry Unlike plane Trigonometry, elementary Spherical Trigonometry is three dimensional.
If based in spherical geometry, the math of Spherical Trig gets downright grisly.
Spiral Sometimes Spiral is used to describe a helix.
A genuine Spiral is a plane figure of changing radius from a (usually fixed) origin.
SSA Ambiguity Side-Side-Angle congruence is not enough to establish congruence between two triangles; it is the Ambiguous case.
SSS Congruence Two triangles whose corresponding sides are congruent are themselves congruent.
SSS Similarity When corresponding sides of two triangles are in a fixed ratio the triangles are similar.
Standard Position An angle in Standard Position has been rotated counterclockwise (for positive rotation) from an initial ray on the positive x-axis.
Straight Angle An angle of 180 degrees or pi radians.
Supplementary Supplementary angles sum to 180 degrees, or pi radians.
Symmetry Having a like but reversed profile or image (a mirror image) about a line is having the quality of Symmetry about the axis (of Symmetry).
Tangent A line that touches a function curve at a single point is said to be Tangent to the function.
Tangent is also one of the six basic trigonometric functions; it is the ratio of the opposite side (from a specified angle) of a right triangle to the adjacent side.
Tangent Line A Line is said to be Tangent to a function when it touches the graph of the function at a single point.
Terminal Side of an Angle When in standard position, an Angle has an initial side, a ray on the positive x-axis, and a Terminal Side where the rotation of the angle stops, at an angle of specific measure (in degrees or radians).
Tetrahedron A polyhedron with four faces.
Theta The eighth letter of the Greek alphabet is Theta, a common variable for an angle.
Three Dimensions The Dimensions of space or volume are Three Dimensions, typically labeled with rectangular, spherical, or cylindrical coordinates.
Three-Dimensional Coordinates Three-Dimensional Coordinates require an ordered triple to label a point in space.
Triangle A three-sided polygon.
Triangles are either acute, right, or obtuse.
Triangulation We may conduct geographic surveys or determine the altitude of various objects by a process termed Triangulation.
Trigonometric Identities The various statements in Trigonometry that are universally true, typically for any angle in the statement, are called Trigonometric Identities.
For example, sin²x + cos²x = 1 for any angle x.
Trigonometry One of the more beautiful and elegant branches of mathematics, Trigonometry provides innumerable relationships built from similar (right) triangles.
Unit Circle A Circle of radius one centered at the origin is termed the Unit Circle.
Unit Vector A vector of length one directed along one of the coordinate axes.
Upper Bound The greatest permissible value of a function may be termed its Upper Bound.
Vector Often represented with an arrow, a Vector is a quantity with both magnitude (size) and direction.
Verify To confirm is to Verify.
When we Verify, we prove or establish some assertion to a dependable conclusion independent from bias.
There is wisdom in these words: "Trust, but Verify."
Vertex A "corner" of a polygon is a Vertex; an extremum of a conic section is a Vertex; the endpoint(s) of rays that form an angle is a Vertex.
Vertical Straight up, perpendicular to horizontal, is Vertical.
Vertical lines have an indeterminate or infinite slope.
Vertical Angles When two lines cross (intersect) they form two pairs of Vertical Angles; the Angles within each pair of Vertical Angles are congruent.
Wavelength The length of a wave, literally, is its Wavelength.
Typically symbolized with Greek letter lambda, a Wavelength can be measured by actual length, or by the period, which may be the angle traversed through one complete cycle, or the time required to complete a cycle.

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