Trigonometry Glossary

AAS reference to solving a triangle given the measure of two angles and the length of a non-included side.

absolute value of a complex number square root of the sum of the squares of its real and imaginary coefficients.

algebraic vector an ordered pair of numbers representing the terminal point of a standard vector.

amplitude of a complex number same as the argument of a complex number.

amplitude the vertical stretch of a function.

angle a measure of rotation.

angle of depression an angle measured below the horizontal.

angle of elevation an angle measured above the horizontal.

angular velocity defined in terms of angle of rotation and time.

argument of a complex number angle formed between the positive x-axis and a line segment between the origin and the number.

ASA reference to solving a triangle given the measure of two angles and the length of the included side.

ASTC an acronym representing which trigonometric functions are positive in the I, II, III, and IV quadrants respectively.

asymptotes lines representing undefined values for trigonometric functions.

bearing an angle measured clockwise from due north to a vector.

circular functions functions whose domains are angles measured in radians and whose ranges are values that correspond to analogous trigonometric functions.

cofunction identities fundamental identities that involve the basic trig functions of complementary angles.

cofunctions pairs of trigonometric functions of complimentary angles whose trigonometric ratios are equal.

complex plane a coordinate system for complex numbers.

component vectors the horizontal and vertical component vectors of a given vector.

components of an algebraic vector the ordered pair of numbers representing the vector.

components the individual vectors that are combined to yield the resultant vector.

conditional equation an equation that is valid for a limited number of values of the variable.

conditional trigonometric equations true for only a limited number of replacement values.

conjugate of a complex number same as original except for the sign of the imaginary component.

cosecant the reciprocal of the sine function.

cosine a trigonometric ratio equal to the adjacent side divided by the hypotenuse.

cotangent the reciprocal of the tangent function.

coterminal two angles in standard position that share a terminal side.

De Moivre's theorem a theorem involving powers of complex numbers.

degree a unit of angle measurement equal to 1/360 of a revolution.

difference identities for tangent identities involving the tangents of differences of angles.

difference identity for cosine one of the trigonometric addition identities.

difference identity for sine one of the trigonometric addition identities.

directed line segment a line segment of a given length and a given direction.

dot product a process of combining two vectors yielding a single number.

double-angle identities for tangent useful in writing trig functions involving double angles as functions of single numbers.

double-angle identities useful in writing trig functions involving double angles as trig functions of single angles.

equivalent vectors two vectors that have the same magnitude and direction.

even function a function is even if f(-x) = f(x).

general solution solutions defined over entire domain.

geometric vector a quantity that can be represented by a directional line segment.

half-angle identities for tangent useful in writing trig functions involving half angles as functions of single angles.

half-angle identities useful in writing trig functions involving half angles as trig functions of single angles.

Heron's formula a formula for finding the area of a triangle given the lengths of the three sides.

identities for negatives fundamental identities that involve the basic trig functions of negative angles.

identity an equation made up of trigonometric functions of an angle that is valid for all values of the angle Also called trigonometric identity.

imaginary axis an axis in the complex plane.

initial point the beginning point of a vector.

initial side side of angle where angle measurement begins.

inverse cosecant function defined in terms of the restricted sine function.

inverse cosine function inverse of the restricted cosine function.

inverse cotangent function defined in terms of the restricted tangent function.

inverse notation notation used to express an angle in terms of the value of trigonometric functions.

inverse secant function defined in terms of the restricted cosine function.

inverse sine function inverse of the restricted sine function.

inverse tangent function inverse of the restricted tangent function.

law of cosines a relationship between the lengths of the three sides of a triangle and the cosine of one of the angles.

law of sines a relationship between the ratios of the sines of angles of a triangle and the side opposite those angles.

linear interpolation a method of approximating values in a table using adjacent table values.

linear velocity defined in terms of arc length and time.

magnitude of a vector the length of the directional line segment.

mathematical induction a method of mathematical proof.

maximum value largest value of a function in a given interval.

minimum value smallest value of a function in a given interval.

minute an angle measurement equal to 1/60 of a degree.

modulus of a complex number same as absolute value of a complex number.

negative angle results from clockwise rotation.

norm another name for the magnitude of a vector.

nth root theorem an extension of De Moivre's theorem involving roots of complex numbers.

odd function a function is odd of f(-x) = -f(x).

odd-even identities fundamental identities that involve the basic trig functions of negative angles. Also called identities for negatives.

one-to-one a characteristic of functions where each element in the domain is pairs with one and only one element in the range and vice versa.

orthogonal perpendicular.

parallelogram rule a process used to add together two nonparallel vectors.

period the smallest value of q such that f(x) = f(x+q) where f(x) is a periodic function.

periodic functions trigonometric functions whose values repeat once each period.

phase shift the horizontal displacement of a function to the right or left of the vertical axis.

polar axis a ray extending from the pole in a polar coordinate system.

polar coordinate system a coordinate system using distance and angle for position.

polar coordinates an ordered pair consisting of a radius and an angle.

pole the fixed center of the polar coordinate system.

position vector another name for a standard vector.

positive angle results from counterclockwise rotation.

primary solutions solutions defined over a limited domain.

principal nth root the unary root of a complex number.

product-sum identities useful in writing the product of trig functions as the sum and difference of trig functions.

projections another name for component vectors, the horizontal and vertical component vectors of a given vector.

proving the identity showing the validity of one identity by using previously known facts.

Pythagorean identities fundamental identities that relate the sine and cosine functions and the Pythagorean Theorem.

quadrantal angle an angle in standard position with its terminal side on a coordinate axis.

quotient identities fundamental identities that involve the quotient of basic trig functions.

radian the measure on an angle with vertex at the center of a circle that subtends an arc equal to the radius of the circle.

radius vector another name for a standard vector, a vector in standard position.

real axis an axis in the complex plane.

reciprocal identities fundamental identities that involve the reciprocals of basic trig functions.

reduction formulas for cosine useful in rewriting cosines of angles greater than 90° as functions of acute angles.

reduction formulas for sine useful in rewriting sines of angles greater than 90° as functions of acute angles.

reduction formulas for tangent useful in rewriting tangents greater than 90° as functions of acute angles.

reference angle an acute angle whose trigonometric ratios are the same (except for sign) as the given angle.

resultant vector the result obtained after vector manipulation.

SAS reference to solving a triangle given the lengths of two sides and the measure of the included angle.

scalar multiplication changing the magnitude of a vector without changing its direction.

scalar multiplication of algebraic vectors a processes of multiplying vector components.

scalar quantity the value of a dot product of two vectors.

secant the reciprocal of the cosine function.

second an angle measurement equal to 1/60 of a minute.

sector a portion of a circle enclosed by a central angle and its subtended arc.

semiperimeter one-half the perimeter of a triangle.

similar triangles two triangles whose angle measurements are the same.

simple harmonic motion a component of uniform circular motion.

sine a trigonometric ratio equal to the opposite side divided by the hypotenuse.

solving the triangle a process for finding the values of sides and angles of a triangle given the values of the remaining sides and angles.

SSA reference to solving a triangle given the lengths of two sides and the measure of a non-included angle.

SSS reference to solving a triangle given the lengths of the three sides.

standard position (angle) an angle with its initial side on the positive x-axis and vertex at the origin.

standard position (vector) a vector that has been translated so that its initial point is at the origin.

standard vector a vector in standard position.

static equilibrium the sum of all the force vectors add up to zero.

sum identities for tangent identities involving the tangents of sums of angles.

sum identity for cosine one of the trigonometric addition identities.

sum identity for sine one of the trigonometric addition identities.

sum-product identities useful in writing the sum and difference of trig functions as the product of trig functions.

tangent a trigonometric ratio equal to the opposite side divided by the adjacent side.

terminal point the ending point of a vector.

terminal side side of angle where angle measurement ends.

tip-tail rule a process for doing vector addition.

trigonometric addition identities identities involving the trig functions of sums and differences of angles.

trigonometric identity an equation made up of trigonometric functions of an angle that is valid for all values of the angle.

trigonometric ratios the ratios of the length of two side of a right triangle.

uniform circular motion circular motion about a point at a uniform linear and angular velocity.

unit circle a circle with a radius of one unit.

vector addition process of combining two vectors.

vector quantity a quantity that has both size and direction.

velocity vector a vector representing the speed and direction of a moving object.

vertical shift the vertical displacement of a function above or below the horizontal axis.

zero algebraic vector an algebraic vector whose components are both zero.

zero vector a vector with a magnitude of zero and any direction.