Trigonometry functions

→"Sine" function :-
          - If function f is f:R -> C , f(a)=p(a) =p(x,y) and h(p(x,y)) = y . so that hof:R →R is called
            sine function and is also known as "sin".

          - Region :- [-1,1]

          - Set of zero :- {kπ / k∈Z}

         

→"cosine" function :-
          - If function f is f:C→R , f(a)=p(a) , p(x,y) and g:c→R,and g(p(x,y))=x.so that gof:R→R is
            called cosine function.cosine function is shortly known as "cos".

          - Region :- [-1,1]

          - Set of zero :-{[(2k + 1)*π/2] /k belongs to set Z} OR {[(2k + 1)*π/2] / k∈Z}

  → "Tangent" function :-

          - Tangent function is also known as "Tan". and   Tanθ = Sinθ / cosθ

          - Region :- R

          - Set of zero :- R - {(2k+1)π/2  / k∈Z}

 →"Cot" function :-
          - cot A = cosθ /sinθ
          - Region :- R
          - Set of zero :- R-{kπ / k∈Z}
 → "Secant" function :-
          - secant function is also known as sec function and is inverse of cosine function.
            secθ= 1/cosθ
          - Region :- R - (-1,1)
         
 →"Cosec" function :-
          - cosec function is inverse of sine function. cosecθ = 1/sinθ
          - Region :- R - (-1,1)
  
→  Here is some formulas regarding to trignometry functions.which will helpful to solve many problems.must remember this.
        . sin^2 A + cos^2 A = 1
        . sec^2 A - tan^2 A = 1
        . cosec^2 A - cot^2 A =1
        . (a+b)^2 = (a-b)^2 - 4ab
        . tanAcotA = secAcosA=sinAcosecA=l
        . sin(π/2 - θ) = cosθ
        . cos(π/2 - θ) = sinθ
        . tan(π/2 - θ) = cotθ
        . sin 15 = cos 75=(√6 - √2) / 4
       . sin 18 = cos72 =(√5 -1) / 4
       . sin36 = cos 54 =(√(10 - 2√5)) / 4
       . sin 54 = cos 36 =(√5 + 1) / 4
       . sin 75 = cos 15 = (√6 + √2) / 4
        . for more formulas see this figure.