#### Chapter 8 Definitions

geometric mean

for the positive numbers a and b, the positive number x such that a / x = x / b. In a geometric sequence, a term that comes between two given nonconsecutive terms of the sequence.

trigonometric ratio

A ratio of two sides of a right triangle.

sine

In a right triangle, the ratio of the length of the leg opposite angle A to the length of the hypotenuse.

cosine

In a right triangle, the cosine of angle A is the ratio of the length of the leg adjacent to angle A to the length of the hypotenuse. It is the reciprocal of the secant function.

tangent of an angle

In a right triangle, the ratio of the length of the leg opposite angle A to the length of the leg adjacent to angle A.

angle of elevation

The angle formed by a horizontal line and a line of sight to a point above.

angle of depression

The angle formed by a horizontal line and a line of sight to a point below.

vector

A quantity that has both magnitude and direction.

component form

The form of a vector that lists the vertical and horizontal change from the initial point to the terminal point.

magnitude

The length of a vector, written | vector AB | or | vector v |.

direction of a vector

The orientation of a vector, which is determined by the angle the vector makes with a horizontal line.

equal vectors

Two vectors that have the same magnitude and the same direction.

parallel vectors

Vectors with the same or opposite direction.

resultant vector

The vector that represents the sum of two given vectors.

reference angle

For an angle in standard position, the reference angle is the positive acute angle formed by the terminal side of the angle and the x-axis.

unit circle

A circle with a radius of 1, centered at the origin.

secant of an angle

In a right triangle, the ratio of the length of the hypotenuse to the length of the side adjacent to angle A. It is the reciprocal of the cosine function.

cosecant

In a right triangle, the cosecant of angle A is the ratio of the length of the hypotenuse to the length of the side opposite A. It is the reciprocal of the sine function.

cotangent

In a right triangle, the cotangent of angle A is the ratio of the length of the side adjacent to A to the length of the side opposite A. It is the reciprocal of the tangent function.