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
From Quotient Relations of Trigonometric Ratios to HOME PAGE
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.
Jul 12, 24 03:08 PM
Jul 12, 24 02:11 PM
Jul 12, 24 03:21 AM
Jul 12, 24 12:59 AM
Jul 12, 24 12:30 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.