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
- 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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