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.

Quotient Relations of Trigonometric Ratios

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

10th Grade Math

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