Trigonometric Equations Study Cards

Enhance Your Learning with Trigonometric Equations Flash Cards for quick learning



Trigonometric Equation

An equation that involves trigonometric functions of an unknown angle.

Sine Function

A trigonometric function that represents the ratio of the length of the side opposite a given angle to the length of the hypotenuse in a right triangle.

Cosine Function

A trigonometric function that represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Tangent Function

A trigonometric function that represents the ratio of the length of the side opposite a given angle to the length of the adjacent side in a right triangle.

Cosecant Function

The reciprocal of the sine function, equal to the ratio of the length of the hypotenuse to the length of the side opposite a given angle in a right triangle.

Secant Function

The reciprocal of the cosine function, equal to the ratio of the length of the hypotenuse to the length of the adjacent side in a right triangle.

Cotangent Function

The reciprocal of the tangent function, equal to the ratio of the length of the adjacent side to the length of the side opposite a given angle in a right triangle.

Trigonometric Identity

An equation that is true for all values of the variables within its domain.

Pythagorean Identity

A trigonometric identity that relates the three basic trigonometric functions in a right triangle: sin^2θ + cos^2θ = 1.

Sum and Difference Identities

Trigonometric identities that express the sine, cosine, and tangent of the sum or difference of two angles in terms of the sine, cosine, and tangent of the individual angles.

Double Angle Identities

Trigonometric identities that express the sine, cosine, and tangent of twice an angle in terms of the sine, cosine, and tangent of the angle.

Half Angle Identities

Trigonometric identities that express the sine, cosine, and tangent of half an angle in terms of the sine, cosine, and tangent of the angle.

Inverse Trigonometric Functions

Functions that give the angle whose trigonometric function value is a given number.

Arcsine Function

The inverse function of the sine function, denoted as sin^(-1)(x) or asin(x).

Arccosine Function

The inverse function of the cosine function, denoted as cos^(-1)(x) or acos(x).

Arctangent Function

The inverse function of the tangent function, denoted as tan^(-1)(x) or atan(x).

Arccosecant Function

The inverse function of the cosecant function, denoted as csc^(-1)(x) or acsc(x).

Arcsecant Function

The inverse function of the secant function, denoted as sec^(-1)(x) or asec(x).

Arccotangent Function

The inverse function of the cotangent function, denoted as cot^(-1)(x) or acot(x).

General Solution

The set of all possible solutions to a trigonometric equation.

Principal Solution

The solution to a trigonometric equation that lies within a specified interval.

Periodic Function

A function that repeats its values in regular intervals.

Period

The smallest positive value of x for which a periodic function f(x) repeats.

Amplitude

The maximum absolute value of a periodic function.

Phase Shift

The horizontal displacement of a periodic function.

Vertical Shift

The vertical displacement of a periodic function.

Trigonometric Equation with Multiple Angles

An equation that involves multiple angles, such as sin(2x) or cos(3x).

Trigonometric Equation with Inverse Trigonometric Functions

An equation that involves inverse trigonometric functions, such as sin^(-1)(x) or cos^(-1)(x).

Trigonometric Equation with Quadratic Terms

An equation that involves quadratic terms of trigonometric functions, such as sin^2(x) or cos^2(x).

Trigonometric Equation with Exponential Terms

An equation that involves exponential terms of trigonometric functions, such as e^(ix) or e^(-ix).

Trigonometric Equation with Logarithmic Terms

An equation that involves logarithmic terms of trigonometric functions, such as log(sin(x)) or log(cos(x)).

Trigonometric Equation with Absolute Value

An equation that involves absolute value of trigonometric functions, such as |sin(x)| or |cos(x)|.

Trigonometric Equation with Rational Functions

An equation that involves rational functions of trigonometric functions, such as sin(x)/cos(x) or cos(x)/sin(x).

Trigonometric Equation with Radical Terms

An equation that involves radical terms of trigonometric functions, such as sqrt(sin(x)) or sqrt(cos(x)).

Trigonometric Equation with Complex Numbers

An equation that involves complex numbers in trigonometric functions, such as sin(ix) or cos(ix).

Trigonometric Equation with Parametric Equations

An equation that involves parametric equations of trigonometric functions, such as x = sin(t) or y = cos(t).

Trigonometric Equation with Series

An equation that involves series representation of trigonometric functions, such as sin(x) = x - (x^3)/3! + (x^5)/5! - ...

Trigonometric Equation with Integral

An equation that involves integral of trigonometric functions, such as ∫sin(x) dx = -cos(x) + C.

Trigonometric Equation with Differential Equation

An equation that involves differential equation of trigonometric functions, such as d^2y/dx^2 + y = 0.

Trigonometric Equation with Limit

An equation that involves limit of trigonometric functions, such as lim(x->0) sin(x)/x = 1.

Trigonometric Equation with Derivative

An equation that involves derivative of trigonometric functions, such as d/dx sin(x) = cos(x).

Trigonometric Equation with Integral Equation

An equation that involves integral equation of trigonometric functions, such as ∫sin(x) dx = x + C.

Trigonometric Equation with Differential Equation System

A system of equations that involves differential equations of trigonometric functions, such as dy/dx = y and dz/dx = z.

Trigonometric Equation with Infinite Series

An equation that involves infinite series of trigonometric functions, such as sin(x) = x - (x^3)/3! + (x^5)/5! - ...

Trigonometric Equation with Matrix

An equation that involves matrix representation of trigonometric functions, such as A*sin(x) = B*cos(x).

Trigonometric Equation with Vector

An equation that involves vector representation of trigonometric functions, such as |A|*|B|*sin(θ) = |A x B|.

Trigonometric Equation with Complex Analysis

An equation that involves complex analysis of trigonometric functions, such as Res(f, z) = 0.

Trigonometric Equation with Differential Geometry

An equation that involves differential geometry of trigonometric functions, such as κ = 1/R.

Trigonometric Equation with Fourier Analysis

An equation that involves Fourier analysis of trigonometric functions, such as f(x) = ∑[n=-∞ to ∞] c_n * e^(inx).

Trigonometric Equation with Laplace Transform

An equation that involves Laplace transform of trigonometric functions, such as L{sin(t)} = 1/(s^2 + 1).

Trigonometric Equation with Z-Transform

An equation that involves Z-transform of trigonometric functions, such as Z{sin(n)} = z/(z^2 - 2z*cos(n) + 1).

Trigonometric Equation with Differential Calculus

An equation that involves differential calculus of trigonometric functions, such as d(sin(x))/dx = cos(x).

Trigonometric Equation with Integral Calculus

An equation that involves integral calculus of trigonometric functions, such as ∫cos(x) dx = sin(x) + C.

Trigonometric Equation with Vector Calculus

An equation that involves vector calculus of trigonometric functions, such as ∇ x F = 0.