text: # trigonometric linearization
  
  ## Calculus linearization_trigo
  
  Calculus in processing ... please wait
  
  ### 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)
explanation: The document provides a detailed explanation of trigonometric linearization, including the use of Euler's formula and the process of linearizing expressions involving powers of sine and cosine. It also describes the syntax and usage of a calculator function called `linearization_trigo` for performing these linearizations. The document does not contain a specific question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: # trigonometric linearization
  
  ## Calculus linearization_trigo
  
  Calculus in processing ... please wait
  
  ### 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)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a detailed explanation of trigonometric linearization, including the use of Euler's formula and the process of linearizing expressions involving powers of sine and cosine. It also describes the syntax and usage of a calculator function called `linearization_trigo` for performing these linearizations. The document does not contain a specific question or a question and answer.
  
  Label: no-question