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**

**Basic Trigonometric Ratios and Their Names****Restrictions of Trigonometrical Ratios****Reciprocal Relations of Trigonometric Ratios****Quotient Relations of Trigonometric Ratios****Limit of Trigonometric Ratios****Trigonometrical Identity****Problems on Trigonometric Identities****Elimination of Trigonometric Ratios****Eliminate Theta between the equations****Problems on Eliminate Theta****Trig Ratio Problems****Proving Trigonometric Ratios****Trig Ratios Proving Problems****Verify Trigonometric Identities****Trigonometrical Ratios of 0°****Trigonometrical Ratios of 30°****Trigonometrical Ratios of 45°****Trigonometrical Ratios of 60°****Trigonometrical Ratios of 90°****Trigonometrical Ratios Table****Problems on Trigonometric Ratio of Standard Angle****Trigonometrical Ratios of Complementary Angles****Rules of Trigonometric Signs****Signs of Trigonometrical Ratios****All Sin Tan Cos Rule****Trigonometrical Ratios of (- θ)****Trigonometrical Ratios of (90° + θ)****Trigonometrical Ratios of (90° - θ)****Trigonometrical Ratios of (180° + θ)****Trigonometrical Ratios of (180° - θ)****Trigonometrical Ratios of (270° + θ)****Trigonometrical Ratios of (270° - θ)****Trigonometrical Ratios of (360° + θ)****Trigonometrical Ratios of (360° - θ)****Trigonometrical Ratios of any Angle****Trigonometrical Ratios of some Particular Angles****Trigonometric Ratios of an Angle****Trigonometric Functions of any Angles****Problems on Trigonometric Ratios of an Angle****Problems on Signs of Trigonometrical Ratios**

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