0Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To solve the questions of trigonometry first, we need to learn all the trigonometric formulas. Now, the exact methods are explained below:
1. Basic formula
Sin, cos, tan - SOH CAH TOA
Sin ø = side opposite to angle ø /hypotenuse
Cos ø = side adjacent to angle ø /hypotenuse
Tan ø = side opposite to angle ø / side adjacent to angle ø
For cot ,sec & cosec
cosec ø = 1 / sin ø
Sec ø = 1 / cos ø
Cot ø = 1 / tan ø
sin, cos, tan at 0, 30, 45, 60 degrees
| 0 | 30 | 45 | 60 | 90 | |
| sin ø | o | 1/2 | 1/√2 | √3/2 | 1 |
| cos ø | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan ø | o | 1/√3 | 1 | √3 | not defined |
| cosec ø | not defined | 2 | √2 | 2/√3 | 1 |
| sec ø | 1 | 2/√3 | √2 | 2 | not defined |
| cot ø | not defined | √3 | 1 | 1/√3 | 0 |
2. Trigonometric Identities :
sin²ø + cos²ø = 1
1+ tan²ø = sec²ø
1+ cot²ø = cosec²ø
3. Sign of sin, cos, tan in different quadrants :
To learn the sign of sin, cos tan in different quadrants, we remember:
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Representing as a table
|
Quadrant I |
Quadrant II |
Quadrant III |
Quadrant IV |
|
|
sin |
+ |
+ |
– |
– |
|
cos |
+ |
– |
– |
– |
|
tan |
+ |
– |
+ |
– |
