# Quotient Relations of Trigonometric Ratios

Quotient relations of trigonometric ratios are tan θ = sin θ/cos θ and cot θ = cos θ/sin θ.

Let OMP be a right angled triangle at M and ∠MOP = θ.

According to the definition of trigonometric ratios we have,

sin θ = perpendicular/hypotenuse = MP/OP ………….. (i)

and cos θ = adjacent/hypotenuse = OM/OP ………….. (ii)

Now dividing (i) by (ii) we get;

sin θ/cos θ = (MP/OP)/(OM/OP)

= (MP/OP) × (OP/OM)

= MP/OM

= tan θ

Therefore, tan θ = sin θ/cos θ

Again dividing (ii) by (i) we get;

cos θ/sin θ = (OM/OP)/(MP/OP)

= (OM/OP) × (OP/MP)

= OM/MP

= cot θ

Therefore, cot θ = cos θ/sin θ

The above step-by-step explanation on quotient relations of trigonometric ratios is very important to solve various problems on trigonometry.

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. ### Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

Jul 12, 24 03:08 PM

The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

2. ### Worksheet on Fractions | Questions on Fractions | Representation | Ans

Jul 12, 24 02:11 PM

In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced

3. ### Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

Jul 12, 24 03:21 AM

There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1…

4. ### Conversion of Improper Fractions into Mixed Fractions |Solved Examples

Jul 12, 24 12:59 AM

To convert an improper fraction into a mixed number, divide the numerator of the given improper fraction by its denominator. The quotient will represent the whole number and the remainder so obtained…