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.
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 / cos q
properties of a secant trigonometry functions are
Sec (−x) = sec x
It is the relations between the cosine and sine functions are the co-function of the
one another.
Sec A = cos (90° - x)
y = f (x) = sec x.
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.
Solution:
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.
Solution:
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
Solution:
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.