# Limit of Trigonometric Ratios

In limit of trigonometric ratios we will learn how to find the limits to the values of sin θ, csc θ, cos θ, sec θ, tan θ and cot θ.

According to the definitions of the trigonometrical ratios of a positive acute angle are always positive.

Note:

Remember that the trigonometrical ratios may be positive as well as negative.

We get from the definitions of trigonometrical ratios that,

Sin θ = PM/OP and Cos θ = OM/OP …….. (A)

From the above picture, OP is the hypotenuse of the triangle POM; hence, PMOP and OMOP.

Therefore, from (A) we get the values of sin θ and cos θ cannot be greater than 1.

Again, csc θ = OP/PM and sec θ = OP/OM

Therefore, it is clearly seen that the values of csc θ and sec θ can never be less than 1.

Finally, tan θ = PM/OM and cot θ = OM/PM

In this case, the values of PM may be greater or less or equal to the values of OM. Thus, the values of tan θ or cot θ may have any non-negative value.

Therefore, the limit of trigonometric ratios of a positive acute angle θ is always non-negative:

(i) The values of sin θ and cos θ cannot be greater than 1;

(ii) The values of csc θ and sec θ cannot be less than 1; and

(iii) The values of tan θ and cot θ can have any value.

Trigonometric Functions

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Fraction as a Part of Collection | Pictures of Fraction | Fractional

Feb 24, 24 04:33 PM

How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

2. ### Fraction of a Whole Numbers | Fractional Number |Examples with Picture

Feb 24, 24 04:11 PM

Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

3. ### Identification of the Parts of a Fraction | Fractional Numbers | Parts

Feb 24, 24 04:10 PM

We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

4. ### Numerator and Denominator of a Fraction | Numerator of the Fraction

Feb 24, 24 04:09 PM

What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.