Lesson 5 Trigonometry - Vocabulary

Damping Factor

A damped trigonometric function is of the form y = f(x)*sin bx or y = f(x)*cos bx, where f(x) is the damping factor.

Sector

A sector of a circle is a region bounded by a central angle and its intercepted arc.

Unit Circle

A unit circle is a circle of radius 1 centered at the origin.

Midline

After a vertical shift, a new horizontal axis known as the midline becomes the reference line or equilibrium point about which the graph oscillates.

Vertex

An angle is defined as two noncollinear rays that share a common endpoint know as a vertex.

Angle of Depression

An angle of depression is the angle formed by a horizontal line and an observer's line of sight to an object below.

Damped Harmonic Motion

An object is in damped harmonic motion when the amplitude is determined by the function a(t) = ke^(-ct).

Oblique Triangle

An oblique triangle is a triangle that is not a right triangle.

Sinusoid

Any transformation of a sine function (or cosine function) is called a sinusoid.

Arccosine Function

Because angles and arcs on the unit circle have equivalent radian measures, the inverse cosine function y = cos^-1 (x) is also referred to as the arccosine function y = arccos x.

Arcsine Function

Because angles and arcs on the unit circle have equivalent radian measures, the inverse sine function y = sin^-1 (x) is also referred to as the arcsine function y = arcsin x.

Arctangent Function

Because angles and arcs on the unit circle have equivalent radian measures, the inverse tangent function y = tan^-1 (x) is also referred to as the arctangent function y = arctan x.

Cosecant

Cosecant (θ) = csc θ = hypotenuse / opposite side or 1/sin θ.

Cosine

Cosine (θ) = cos θ = adjacent side / hypotenuse.

Cotangent

Cotangent (θ) = cot θ = adjacent side / opposite side or 1/tan θ .

Coterminal Angles

Coterminal angles are two angles that have the same initial and terminal sides, but different measures.

Periodic Function

Functions with values that repeat at regular intervals are called periodic functions.

Ambiguous Case

Given the measures of two sides and a nonincluded angle, one of the following will be true: (1) no triangle exists, (2) exactly one triangle exists, or (3) two triangles exist. For this ambiguous case, there may be no solution, one solution or two solutions.

Heron's Formula

Heron's Formula says the area of an oblique triangle is equal to the square root of [s(s - a)(s - b)(s - c)] where s is the semi-perimeter (s = 1/2(a + b + c)) .

Inverse Cosine

If θ is an acute angle and the cosine of θ is x, then the inverse cosine of x is the measure of angle θ. If cos θ = x, then cos^-1 (x) = θ.

Inverse Sine

If θ is an acute angle and the sine of θ is x, then the inverse sine of x is the measure of angle θ. If sin θ = x, then sin^-1 (x) = θ.

Inverse Tangent

If θ is an acute angle and the tangent of θ is x, then the inverse tangent of x is the measure of angle θ. If tan θ = x, then tan^-1 (x) = θ.

Reference Angle

If θ is an angle in standard position, its reference angle θ' is the acute angle formed by the terminal side of θ and the x-axis.

Standard Position

In the coordinate plane, an angle with its vertex at the origin and its initial side along the positive x-axis is said to be in standard position.

Secant

Secant (θ) = sec θ = hypotenuse / adjacent side or 1/cos θ .

Radian

Since a degree has no relationship to any linear measure, measuring angles in radians solves this issue. Radians is measure in terms of Π, such that 180 degrees = 2Π radians.

Sine

Sine (θ) = sin θ = opposite side / hypotenuse.

Solve a Triangle

Solve a triangle means to find the measures of all of the sides and angles of the triangle.

Tangent

Tangent (θ) = tan θ = opposite side / adjacent side.

Law of Cosines

The Law of Cosines says a^2 = b^2 + c^2 - 2bc*cos A and can be used to solve oblique triangles if you are given the measures of three sides (SSS) or two sides and their included angle (SAS).

Law of Sines

The Law of Sines says sin A/a = sin B/b = sin C/c and can be used to solve oblique triangles if you know the measures of two angles and a nonincluded side (AAS), two angles and the included side (ASA), or two sides and nonincluded angle (SSA).

Amplitude

The amplidtude of a sinusoidal function is half the distance between the maximum and minimum values of the function or half the height of the wave. This is the |a| value in the sinusoidal function formula: y = a sin b(θ - c) + d.

Reciprocal Function

The cosecant, secant, and cotangent functions are called reciprocal functions because their ratios are the reciprocals of the sine, cosine, and tangent ratios, respectively.

Frequency

The frequency of a sinusoidal function is the numer of cycles the function completes in a one unit interval. This is the b value in the sinusoidal function formula: y = a sin b(θ - c) + d.

Phase Shift

The phase shift of a sinusoidal function is the difference between the horizontal position of the function and that of the parent sinusoidal function. This is the c value in the sinusoidal function formula: y = a sin b(θ - c) + d.

Linear Speed

The rate at which an object moves along a circular path is called its linear speed.

Angular Speed

The rate at which an object rotates about a fixed point is called its angular speed.

Terminal Side

The second ray's position forms the angle's terminal side.

Period

The smallest number c for which f is periodic is called the period of f.

Initial Side

The starting position of the first ray forms the initial side of the angle.

Vertical Shift

The vertical shift is the vertical translation of the parent sinusoidal function.This is the d value in the sinusoidal function formula: y = a sin b(θ - c) + d.

Trigonometric Functions

Trigonometric ratios use the side measures of a right triangle and a reference angle labeled θ (the Greek letter theta) to form the ratios that define the six trigonometric functions.

Trigonometric Ratios

Trigonometric ratios use the side measures of a right triangle and a reference angle labeled θ (the Greek letter theta) to form the ratios that define the six trigonometric functions.

Damped Trigonometric Function

When a sinusoidal function is multiplied by another function f(x), this product of the two functions is known as a damped trigonometric function. A damped trigonometric function is of the form y = f(x)*sin bx or y = f(x)*cos bx

Inverse Trigonometric Function

When a trigonometric value of an acute angle is known, the coresponding inverse trigonometric function can be used to find the measure of the angle.

Circular Function

When defined as functions of the real number system using the unit circle, the trigonometric funtions are often called circular functions.

Damped Oscillation

When the product of a sinusoidal function and another function reduces the amplitude of the wave of the original sinusoid, it is called damped oscillation or damped wave.

Damped Wave

When the product of a sinusoidal function and another function reduces the amplitude of the wave of the original sinusoid, it is called damped oscillation or damped wave.

Quadrantal Angle

When the terminal side of an angle θ that is in standard position lies on one of the coordinate axes, the angle is called a quadrantal angle.