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.
