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.