Solved Problems Of Trigonometric Inequality

Trigonometry is an essential part of mathematics. It Is widely used to find the sides and value of angles in a triangle. Trigonometry deals with a right-angled triangle. Six main functions come under the study of trigonometry. These are cosine, sine, cosecant, secant, cotangent, and tangent. All these functions in the short form are demonstrated as cos x, sin x, cosec x, sec x, cot x, and tan x. Trigonometry Inequality also comes under the study of triangles. The difference is that the Trigonometry Inequality deals with the different functions of different triangles simultaneously. 

Trigonometry 

Trigonometry is the study of triangles in mathematics. In trigonometry, one deals with a relationship between the angles and sides of any triangle, especially right-angled triangles. It consists of many identities, and trigonometric ratios define these identities. 

Cosecant or Cosec x = Hypotenuse/Perpendicular

• Cotangent or cot x = Base/Perpendicular

• Tangent or tan x = Perpendicular/Base

Trigonometry Inequality

Trigonometry Inequality is an essential topic of trigonometry. It is widely used to deal with the various functions of x at a time. Trigonometry Inequality includes more than one value of function y. Although, the value of function y is written in the standard form, which is described as a: 

R [f(y), g(y)…]

It can either be less than zero or greater than zero. 

Solving the equation in trigonometry Inequality means calculating those values of y, which satisfies the Inequality. The set of solutions in the trigonometry Inequality is demonstrated under the intervals. There are four important trigonometry Inequalities. These are:

• sin y < p (and > p)

• cos y < p (and > p)

• tan y < p (and > p)

• cot y < p (and > p)

In the above statement, p is the constant. 

Steps to find the trigonometric Inequalities:

Let’s understand some important steps to calculate the values of trigonometry Inequality. 

Trigonometry Inequality is a systematic method of finding the more than one value of a variable y in a trigonometric function. So, it also contains some significant steps, which are demonstrated as follows:

Step 1

In mathematics, Inequality means the value which is not equal. Although, there are also some symbols in mathematics that describe the Inequality of any number. So, the first step of solving trigonometric Inequalities is to convert the inequality sign into equality. Like for any cos x Inequality trigonometric functions, convert In into the equality accordingly. 

Step 2 

After converting the Inequality sign to the equality sign, the result will come in a trigonometric equation. Solve that equation. The equation must be solved based on its variable. After that, put different identities and formulas for getting the result. The resulting value will be the value in it. Although, the value must lie within the interval [0, 2π]. For instance, if the result is coming in the form of tan x. Then, the tax x value must lie within the [0, 2π] interval. 

Step 4

If the resulting value of the equating is positive, then it will get changed into the negative also. In this case, both positive and negative values will be considered; only the condition is that the resulting angle must be greater than the π. For instance, if the result is coming in the form of cos x, then – cos x will also be the solution of the trigonometric equation. 

Step 5

After getting the resultant angle of the equation, one has to find the base interval, which lies in between the resultant values. Although, it can be obtained by dividing the sum of values by two. This step will provide an interval to the acquired solution. 

Step 6

After acquiring the intervals, one has to check whether the given Inequality function is asymptotes in the acquired interval or not. 

The interval value at which the Inequality trigonometric functions become asymptotic will limit the whole function. Hence, it will become the solution for the given Inequality trigonometric function.