Trigonometric Ratios and Angles
* Trigonometry is the study of relationship between the angles and sides of triangles.
* The ratios between the lengths of the sides of a right-angled triangle are relation with its acute angles is called trigonometric ratios.
N a right-angled triangle ABC, if ∠A is an acute angle:
* Sin ∠A = \frac{side \thinspace \thinspace opposite \thinspace to \thinspace ∠A}{hypotenuse}
* Cos ∠A = \frac{side \thinspace \thinspace adjecent \thinspace to \thinspace ∠A}{hypotenuse}
* Tan ∠A = \frac{side \thinspace \thinspace opposite \thinspace to \thinspace ∠A}{side \thinspace \thinspace adjacent \thinspace to \thinspace ∠A}
* Cosec ∠A = \frac{1}{sin \thinspace \thinspace ∠A} = \frac{hypotenus}{side \thinspace \thinspace opposite \thinspace to \thinspace ∠A}
* Sec ∠A = \frac{1}{cos \thinspace \thinspace ∠A} = \frac{hypotenus}{side \thinspace \thinspace adjacent\thinspace to \thinspace ∠A}
* Cot ∠A = \frac{1}{tan \thinspace \thinspace ∠A} = \frac{side \thinspace \thinspace adjacent\thinspace to \thinspace ∠A}{side \thinspace \thinspace opposite \thinspace to \thinspace ∠A}
If we know the value of any one of the trigonometric ratios of an acute angle in a right-angled triangle, we can calculate other trigonometric ratios of the angle.
Trigonometric Ratios of Special Angles
| Trigonometric Ratios Of Complementary Angles |
| Sin ( 90° – A ) = cos A |
| Cos ( 90° – A ) = sin A |
| Tan ( 90° – A ) = cot A |
| Cosec ( 90° – A ) = sec A |
| Sec ( 90° – A ) = cosec A |
| Cot ( 90° – A) = tan A |
Trigonometric Identities
An equation that is true for all values of the quantities that it contains is called as identity.
Trigonometric Identities:
* Sin²θ +cos² θ = 1 where 0° ≤ θ ≤ 90°
* 1+ cot²θ = cosec²θ where 0° < θ ≤ 90°
* 1+ tan²θ = sec²θ where 0° ≤ θ< 90°