# 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