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
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