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

10th Grade Math

From Quotient Relations of Trigonometric Ratios to HOME PAGE