Preparation For Secants

Introduction :

             In trigonometry, preparation for secants is a one interesting topic in mathematics. It is a one of the type of trigonometric functions. Trigonometry function for secants can represent the ratio of sides of the triangle. It is also known as circular function. Since the values of a secant can be the ratios of x and y co-ordinates on a circle of radius 1.Let us discuss the preparation for secants and its example problems.



Definition of preparation for secants trigonometry:


Secant of an angle is the ratio of length of the hypotenuse and the opposite side.

                  Sec (q) = hypotenuse / opposite 

The secant is the inverse of the cosine and is given by the relation
sec q = 1 / coq



Properties of a secant trigonometry:


properties of a secant trigonometry functions are

  • The Secant is an even function.

      Sec (−x) = sec x

  • The graph of a secant function is symmetric with y-axis.
  • The period of the secant function is 2`pi` .
  • It has a vertical asymptotic at x = `pi`/2 + k`pi`
  • The Secant function domain is all the real numbers except (`pi`/2, k`pi`)
  • The range of the secant function is ((−∞, -1) to (+1, +∞))
  • Co-function for secant

              It is the relations between the cosine and sine functions are the co-function of the one another.
                              Sec A = cos (90° - x)

  • Graph for Secant function:

               y = f (x) = sec x.



Example problems in preparation for secants:


Some example problems in preparation for secants are

Example 1:

Find the length of the opposite side for the given triangle using the secant function.

                          right triangle


              Trigonometry secant function

               Sec θ = Hypotenuse / opposite

               Using this, we can find the solution for the opposite side

               Sec θ = hyp /opp

               Sec 60° = 4/opp

               Opp = 4/ sec 60°

               Opp = 4/ (2)

               Opp = 2.

Length of the opposite side is 2m.

Example 2:

Find the hypotenuse of the given triangle using the trigonometry secant function.

                         right triangle


               Using the trigonometry secant function

               Sec θ = Hypotenuse / Opposite

               Using this, we can find the solution to the hypotenuse

               Sec θ = hyp / opp

               Sec 30° = hyp/ 2

                   2/√3 = hyp /2

                    hyp = 4√3

Hypotenuse for the given triangle is 4√3 cm.



Example 3:

Find the secant function for the given cos function

Cos 45 = 1/√2


              Given Cos function

                 Cos 45 = 1/√2

               Using the inverse Cosine function relation to find the solution of secant function

                Sec θ = 1/ Cos θ

                Sec 45° = 1/ Cos 45°

                              = 1/ (1/√2)

                Sec 45° = √2.

Solution to the Secant function is √2.