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)
= 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)
= 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