Trigonometric linearization : How to use it?
Calculator that allows to linearize a trigonometric expression.
Syntax :
linearization_trigo(expression), where expression represents the trigonometric expression to be linearized.
Examples :
- linearization_trigo(`cos(x)^2`) returns `(1+cos(2x))/2`
- linearization_trigo(`sin(x)^2`) returns `(1-cos(2x))/2`
Linearize a trigonometric expression is to rewrite this expression in a form that no longer contains exponent. The calculator makes it possible, by various methods, to linearize many forms of trigonomeric expressions. Trigonometric expressions are expressions that involve the functions sinus, cosine, tangent ...
To linearize a trigonometric expression, the calculator is based on the formulas of Euler.
Euler's formula
The Euler's formula makes it possible to establish a relation between the cosine and the exponential on the one hand and between the sinus and the exponential on the other hand. Thus, the formula of Euler makes it possible to write:
- `cos(x)=(e^(ix)+e^(-ix))/2`
- `sin(x)=(e^(ix)-e^(-ix))/(2i)` where i, represents the symbol of complex numbers.
Linearization of expression involving cosine powers
The calculator is able to linearize expressions of the form `cos^n(x)`, where n represents an integer. So to linearize the following trigonometric expression `cos^2(x)`, just enter linearization_trigo(`cos(x)^2`).
Linearization of expression involving sinus powers
The calculator is able to linearize expressions of the form `sin^n(x)`, where n represents an integer. So to linearize the following trigonometric expression `sin^2(x)`, just enter linearization_trigo(`sin(x)^2`).
Application of trigonometric linearization
Trigonometric linearization can be very useful for integral calculation involving sine or cosine powers.
- Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccos function is the inverse functions of the cosine function.
- Arcsine : arcsin. The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine function.
- Arctangent : arctan. The arctan function allows the calculation of the arctan of a number. The arctan function is the inverse functions of the tangent function.
- Trigonometric Calculator : simplify_trig. Calculator wich uses trigonometric formula to simplify trigonometric expression.
- Cosine : cos. The cos trigonometric function calculates the cos of an angle in radians, degrees or gradians.
- Cosecant : cosec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
- Cotangent : cotan. The cotan trigonometric function to calculate the cotan of an angle in radians, degrees or gradians.
- Trigonometric expansion : expand_trigo. The calculator makes it possible to obtain the trigonometric expansion of an expression.
- Trigonometric linearization : linearization_trigo. Calculator that allows to linearize a trigonometric expression.
- Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.
- Secant : sec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
- Sine : sin. The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.
- Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.