Learn definition of sec

Introduction :
Learn definition of Sec is defined as the function which is used to calculate the ratio of sides of the triangle. It is also known as inverse of cos function. Sec is a one kind of trigonometric functions. Sec of an angle is the ratio of hypotenuse and the length of the adjacent side. In other words, the learn definition of Sec is the reciprocal of cos.

In a right angle triangle,

                  Sec(A)=hypotenuse       
                              adjacent side        
               Here A is a angle, Sec (A) = 1/ (cos A)        

Learn definition of sec:

Learn properties of sec angle:
Learn definition of sect is intervallic and repeats itself every 2 radians. An essential property is sec(0)=1. Few other main properties are

By the definition of sec,
           sec x               = 1/cos x
           sec( x + 2 )   = sec (x) sec ( /2)    = ∞ (infinity)
           sec(-x)            = sec(x)
           sec(x)             = i sec h(ix)

Learn important calculus relations of sec:
             d/dx sec(x) = sec(x) tan(x)    (differentiation)
            ∫ sec(x) dx   = ln sec(x) + tan(x) = ln ( /4 + /2)  (integral)

Learn series expansion of the function of sec:
           sec(x)  = 1 + x²/2 + 5x⁴/24 + 61z⁶/ 720 + ..... + (-1)ⁿ E_2n/(2n)! X_2n + ......
Here the E's are the Euler numbers of secant.

Learn domain of sec:
          Every numbers are real except /2 + k , k is an integer.

Learn range of sec:
           (-∞ , -1] U [1 , +∞)

Learn Period of sec:
                 2 π

Learn y intercepts of sec:
           y = 1

Learn of sec symmetry:
           sec(-x) = sec (x).   Because sec (x) is an even function and graph is symmetric.

Learn of sec intervals of increase/decrease:
From 0 to 2, sec (x) is increasing on (0 to /2) U ( /2  to  ) and decreasing on ( to 3 /2) U (3 /2 to 2 ).

Learn vertical asymptotes of sec:
           Vertical asymptote = /2 + k π , where k is an integer.

Learn co function for sec : 
           sec x  = cosec (90^o - x).

Practice problem for learn definition of sec:

Practice problems using learn of secant function:
1. Find the function value of sec 45^o.

Solution:
         Use the Sec's co task identity to solve the problem.
By the definition of sec,
        function for sec is  sec x   = cosec (90^o - x)
                                         sec 30^o= cosec (90^o – 30^o )
                                                      = cosec (60^o)
                                          sec 30^o = 0.866
         The solution of sec of 30^o is 0.866.

2. Find the angle of a right triangle where hypotenuse = 2, length of the adjacent side = 1 using secant function?

  Given:
         In a right angle triangle length of the hypotenuse = 2, length of the adjacent side = 1

  Solution:         
By the definition of sec,
           Sec x  =  hypotenuse/adjacent side
                      = 2 / 1
                   x = sec^-1 (2)
                   x = 60^o 
The secant angle of triangle is 60 degrees.