Restrictions of Trigonometrical Ratios

Some of the Restrictions of Trigonometrical Ratios are:

● If A and B two acute angles and sin A = sin B, then we get A = B. If we cancel sign from both side to get the result, that is wrong.

For Example: If Sin θ = 60°, then θ = 60°. But we should not cancel sign from both sides to get the result.

● Cos 2θ ≠ 2 Cos θ

● Sin A/Sin B ≠ A/B

● Sin A ± Sin B ≠ Sin (A ≠ B)

● Cos θ does not imply cos × θ; in fact, it represents the ratio of perpendicular and hypotenuse with respect to the angle θ of a right-angled triangle.

● Cos² θ means (cos θ)² or cos θ × cos θ; do not write (cos θ)² = cos θ² since cos θ² implies cos (θ × θ).

Similarly we write, sin³ θ for (sin θ)³;
                         tan⁵ θ for (tan θ)⁵;
                         sec⁷ θ for (sec θ)⁷; etc,.

These are the restrictions of trigonometrical ratios need to be followed in case of learning the trigonometric ratios.

● 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

11 and 12 Grade Math

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