Trigonometry is the study of relationships between angles, lengths, and heights of triangles. It includes ratios, function, identities, formulas to solve problems based on it, especially for right-angled triangles. Applications of trigonometry
are also found in engineering, astronomy, Physics and architectural design. This chapter is very important as it comprises many topics like Linear Algebra, Calculus and Statistics.
Applying Pythagoras theorem for the given right-angled triangle, we have:
(Perpendicular)2+(Base)2=(Hypotenuese)2
⇒(P)2+(B)2=(H)2
The Trigonometric properties are given below:
S.no | Property | Mathematical value |
1 | sin A | Perpendicular/Hypotenuse |
2 | cos A | Base/Hypotenuse |
3 | tan A | Perpendicular/Base |
4 | cot A | Base/Perpendicular |
5 | cosec A | Hypotenuse/Perpendicular |
6 | sec A | Hypotenuse/Base |
Relation Between Trigonometric Identities:
S.no | Identity | Relation |
1 | tan A | sin A/cos A |
2 | cot A | cos A/sin A |
3 | cosec A | 1/sin A |
4 | sec A | 1/cos A |
Trigonometric Identities:
- sin2A + cos2A = 1
- tan2A + 1 = sec2A
- cot2A + 1 = cosec2A