Calculator that allows to linearize a trigonometric expression.

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.

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`