# trigonometric linearization

## Calculus linearization_trigo

Calculator that allows to linearize a trigonometric expression.

### Function : linearization_trigo

#### Summary :

Calculator that allows to linearize a trigonometric expression.

linearization_trigo online

#### Description :

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.

Calculator that allows to linearize a trigonometric expression.

#### Syntax :

linearization_trigo(expression), where expression represents the trigonometric expression to be linearized.

#### Examples :

Calculate online with linearization_trigo (trigonometric linearization)
• Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccosine 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 arcsine function is the inverse function of the sine function.
• Arctangent : arctan. The arctan function allows the calculation of the arctangent of a number. The arctangent function is the inverse functions of the tangent function.
• Cosine : cos. The cos trigonometric function calculates the cosine 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 cotangent 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.
• Secant : sec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
• Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.
• Sine : sin. The sin trigonometric function to calculate the sine of an angle in radians, degrees or gradians.
• Tangent : tan. The tan trigonometric function to calculate the tangent of an angle in radians, degrees or gradians.
• Trigonometric Calculator : trig_calculator. Calculator wich uses trigonometric formula to simplify trigonometric expression.