Formulae [2]
Formula: Trigonometric Ratios
\[sineA=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\]
\[cosineA=\frac{\mathrm{Base}}{\text{Hypotenuse}}\]
\[tangentA=\frac{\text{Perpendicular}}{\mathrm{Base}}\]
\[cotangent A = \frac{\text{Base}}{\text{Perpendicular}}\]
\[secantA=\frac{\text{Hypotenuse}}{\mathrm{Base}}\]
\[cosecantA=\frac{\text{Hypotenuse}}{\text{Perpendicular}}\]
Formula: Trigonometrical Ratios of Complementary Angles
For an acute angle A,
- sin (90° - A) = cos A
- cos (90° - A) = sin A
- tan (90° - A) = cot A
- cot (90° - A) = tan A
- sec (90° - A) = cosec A
- cosec (90° - A) = sec A
Theorems and Laws [1]
If tan A = cot B, prove that A + B = 90°.
∵ tan A = cot B
tan A = tan (90° – B)
A = 90° – B
A + B = 90°. Proved
Key Points
Key Points: Trigonometric Ratios
For an acute angle A in a right-angled triangle:
-
Hypotenuse is the side opposite the right angle.
-
Perpendicular is the side opposite angle A.
-
Base is the side adjacent to angle A.
Key Points: Trigonometric Ratios of Specific Angles
| Angle | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan | 0 | 1/√3 | 1 | √3 | Not defined |
| cosec | Not defined | 2 | √2 | 2/√3 | 1 |
| sec | 1 | 2/√3 | √2 | 2 | Not defined |
| cot | Not defined | √3 | 1 | 1/√3 | 0 |
