The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −).

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Term

VERTEX OF AN ANGLE

Definition

Vertex (of an angle) The vertex of an angle is the common endpoint of two rays that form the angle.

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Term

standard Position of an angles

Definition

Angles can exist anywhere in the coordinate plane where two rays share a common vertex. If this vertex is at the origin of the plane and the initial side lies along the positive $x$-axis, then the angle is said to be in standard position.

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Term

Positive and negative angles

Definition

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The measure of an angle describes the magnitude and direction of the rotation of the ray from its initial position to its terminal position. If the rotation is counterclockwise, the angle has a positive measure. If the rotation is clockwise, the angle has a negative measure.

Term

REFERENCE ANGLES

Definition

The reference angle is the angle that the given angle makes with the x-axis. Regardless of where the angle ends (that is, regardless of the location of the terminal side of the angle), the reference angle measures the closest distance of that terminal side to the x-axis.

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Term

Coterminal Angles

Definition

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, the angles 30°, –330° and 390° are all coterminal (see figure 2.1 below).

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Term

unit circle

Definition

In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

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Term

Sine function

Definition

the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse).

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Term

cosine function

Definition

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Cos function (or cosine function) in a triangle is the ratio of the adjacent side to that of the hypotenuse. The cosine function is one of the three main primary trigonometric functions and it is itself the complement of sine(co+sine).

Term

tangent function

Definition

The tangent function is a periodic function which is very important in trigonometry. The simplest way to understand the tangent function is to use the unit circle. ... The x -coordinate of the point where the other side of the angle intersects the circle is cos(θ) and the y -coordinate is sin(θ) .

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Term

Period (of a trigonometric function)

Definition

Period of a Trigonometric Function The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

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Term

Amplitude

Definition

The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of a function

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Term

Frequency

Definition

The frequency of a trigonometric function is the number of cycles it completes in a given interval. This interval is generally 2π radians (or 360º) for the sine and cosine curves.

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Term

Midline

Definition

A midline of a sinusoidal function is the horizontal center line about which the function oscillates above and below. For y = sin x, the midline is y = 0 (the x-axis). The midline is parallel to the x-axis and is located half-way between the graphs maximum and minimum values.

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Term

Domain and range

Definition

the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

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Term

Asymptote

Definition

a line that continually approaches a given curve but does not meet it at any finite distance.