Sine tables
Sine θ is written sin θ nowadays but it is still pronounced sine θ.
Tables of the value of sin θ for varying angles of θ were calculated by an Indian mathematician and astronomer called Madhava. This wasn’t the first time values of sin were calculated but the table is useful for us to look at here. We can see the value of sin θ increasing as θ increases from 3.75 to 90.
|
Angle θ in degrees |
sin θ |
| 3.75 | 0.065 |
| 7.50 | 0.131 |
| 11.25 | 0.195 |
| 15.00 | 0.259 |
| 18.75 | 0.321 |
| 22.50 | 0.383 |
| 26.25 | 0.442 |
| 30.00 | 0.500 |
| 33.75 | 0.556 |
| 37.50 | 0.609 |
| 41.25 | 0.659 |
| 45.00 | 0.707 |
| 48.75 | 0.752 |
| 52.50 | 0.793 |
| 56.25 | 0.831 |
| 60.00 | 0.866 |
| 63.25 | 0.897 |
| 67.50 | 0.924 |
| 71.25 | 0.947 |
| 75.00 | 0.966 |
| 78.75 | 0.981 |
| 82.50 | 0.991 |
| 86.25 | 0.998 |
| 90.00 | 1.000 |
This makes sense because sine θ is just the opposite divided by the hypotenuse and as θ gets bigger, the opposite lengthens more than the hypotenuse.Looking at the table, it is clear that as θ gets larger so does the value of sine θ.
The diagram shows that O lengthens more than H as the angle increases and so O ÷ H increases.
