**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.