Chapter 13

Cotangent

(in a right-angled triangle) the ratio of the side (other than the hypotenuse) adjacent to a particular acute angle to the side opposite the angle.

Tangent

the trigonometric function that is equal to the ratio of the sides (other than the hypotenuse) opposite and adjacent to an angle in a right triangle.

Terminal Side

An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

Angle of Depression

Angle of depression is the angle between the horizontal and the line of sight to an object beneath the horizontal.

Angle of Elevation

Angle of elevation is the angle between the horizontal and the line of sight to an object above the horizontal.

Coterminal Angles

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example 30°, -330° and 390° are all coterminal.

Trigonometric Functions

a function of an angle, or of an abstract quantity, used in trigonometry, including the sine, cosine, tangent, cotangent, secant, and cosecant, and their hyperbolic counterparts.

Law of Cosines

a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

Initial Side

a stationary straight line that contains a point about which another straight line is rotated to form an angle — compare terminal side.

Unit Circle

a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

Radian

a unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius.

Periodic

appearing or occurring at intervals.

Trigonometry

the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Period

the interval between successive equal values of a periodic function.

Standard Position

the position of an angle with its vertex at the origin of a rectangular-coordinate system and its initial side coinciding with the positive x-axis.

Secant

the ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Cosine

the trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.

Sine

the trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse.

Cosecant

In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. In a formula, it is abbreviated to just 'csc'.

Principle Values

In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined.

Reference Angle

In standard position, the reference angle is the smallest angle between the terminal side and the x-axis. The values of the trig functions of angle θ are the same as the trig values of the reference angle for θ, give or take a minus sign.

Quadrantal Angles

Quadrantal Angle. An angle with terminal side on the x-axis or y-axis. That is, the angles 0°, 90°, 180°, 270°, 360°, 450°, ... as well as -90°, -180°, -270°, -360°, ...

Solve a Right Triangle

Techniques for Solving. A right triangle is a triangle with one right angle. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The angles opposite the legs, by definition, are complementary.

Law of Sines

The Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles. Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

Arccosine Function

The arccos function is the inverse of the cosine function. It returns the angle whose cosine is a given number.

Arcsine Function

The arcsin function is the inverse of the sine function. It returns the angle whose sine is a given number.

Arctangent Function

The arctan function is the inverse of the tangent function. It returns the angle whose tangent is a given number.

Circular Function

The arctangent of x is defined as the inverse tangent function of x when x is real (x∈ℝ). When the tangent of y is equal to x: tan y = x. Then the arctangent of x is equal to the inverse tangent function of x, which is equal to y: