Conventionally no relation tangent and cotangent
Notation
Conventionally, an abbreviation of each trigonometric function's name is used as its symbol in formulas. Today, the most common versions of these abbreviations are "sin" for sine, "cos" for cosine, "tan" or "tg" for tangent, "sec" for secant, "csc" or "cosec" for cosecant, and "cot" or "ctg" for cotangent. Historically, these abbreviations were first used in prose sentences to indicate particular line segments or their lengths related to an arc of an arbitrary circle, and later to indicate ratios of lengths, but as the function concept developed in the 17th–18th century, they began to be considered as functions of real-number-valued angle measures, and written with functional notation, for example sin(x). Parentheses are still often omitted to reduce clutter, but are sometimes necessary; for example the expression 
  
    
      
        sin
        ⁡
        x
        +
        y
      
    
    {\displaystyle \sin x+y}
   would typically be interpreted to mean 
  
    
      
        sin
        ⁡
        (
        x
        )
        +
        y
        ,
      
    
    {\displaystyle \sin(x)+y,}
   so parentheses are required to express 
  
    
      
        sin
        ⁡
        (
        x
        +
        y
        )
        .
      
    
    {\displaystyle \sin(x+y).}
  
A positive integer appearing as a superscript after the symbol of the function denotes exponentiation, not function composition. For example 
  
    
      
        
          sin
          
            2
          
        
        ⁡
        x
      
    
    {\displaystyle \sin ^{2}x}
   and 
  
    
      
        
          sin
          
            2
          
        
        ⁡
        (
        x
        )
      
    
    {\displaystyle \sin ^{2}(x)}
   denote 
  
    
      
        sin
        ⁡
        (
        x
        )
        ⋅
        sin
        ⁡
        (
        x
        )
        ,
      
    
    {\displaystyle \sin(x)\cdot \sin(x),}
   not 
  
    
      
        sin
        ⁡
        (
        sin
        ⁡
        x
        )
        .
      
    
    {\displaystyle \sin(\sin x).}
   This differs from the (historically later) general functional notation in which 
  
    
      
        
          f
          
            2
          
        
        (
        x
        )
        =
        (
        f
        ∘
        f
        )
        (
        x
        )
        =
        f
        (
        f
        (
        x
        )
        )
        .
      
    
    {\displaystyle f^{2}(x)=(f\circ f)(x)=f(f(x)).}
  
However, the exponent 
  
    
      
        
          −
          1
        
      
    
    {\displaystyle {-1}}
   is commonly used to denote the inverse function, not the reciprocal. For example 
  
    
      
        
          sin
          
            −
            1
          
        
        ⁡
        x
      
    
    {\displaystyle \sin ^{-1}x}
   and 
  
    
      
        
          sin
          
            −
            1
          
        
        ⁡
        (
        x
        )
      
    
    {\displaystyle \sin ^{-1}(x)}
   denote the inverse trigonometric function alternatively written 
  
    
      
        arcsin
        ⁡
        x
        :
      
    
    {\displaystyle \arcsin x\colon }
   The equation 
  
    
      
        θ
        =
        
          sin
          
            −
            1
          
        
        ⁡
        x
      
    
    {\displaystyle \theta =\sin ^{-1}x}
   implies 
  
    
      
        sin
        ⁡
        θ
        =
        x
        ,
      
    
    {\displaystyle \sin \theta =x,}
   not 
  
    
      
        θ
        ⋅
        sin
        ⁡
        x
        =
        1.
      
    
    {\displaystyle \theta \cdot \sin x=1.}
   In this case, the superscript could be considered as denoting a composed or iterated function, but negative superscripts other than 
  
    
      
        
          −
          1
        
      
    
    {\displaystyle {-1}}
   are not in common use.Etymology
The word sine derives from Latin sinus, meaning "bend; bay", and more specifically "the hanging fold of the upper part of a toga", "the bosom of a garment", which was chosen as the translation of what was interpreted as the Arabic word jaib, meaning "pocket" or "fold" in the twelfth-century translations of works by Al-Battani and al-Khwārizmī into Medieval Latin.
The choice was based on a misreading of the Arabic written form j-y-b (جيب), which itself originated as a transliteration from Sanskrit jīvā, which along with its synonym jyā  (the standard Sanskrit term for the sine) translates to "bowstring", being in turn adopted from Ancient Greek χορδή "string".The word tangent comes from Latin tangens meaning "touching", since the line touches the circle of unit radius, whereas secant stems from Latin secans—"cutting"—since the line cuts the circle.The prefix "co-" (in "cosine", "cotangent", "cosecant") is found in Edmund Gunter's Canon triangulorum (1620), which defines the cosinus as an abbreviation for the sinus complementi (sine of the complementary angle) and proceeds to define the cotangens similarly.
no relation