Trigonometric Tables
Introduction to trigonometric tables :
Trigonometry is a very important mathematical terminology which is used in various situations in our various daily life activities. The word trigonometry was first of all coined by the Indian mathematician. There are mainly six mathematical terms, that is, sin , cosine, tan, cot, sec, cosec. Let me explain this with a figure.
With the help of above three trigonometrical formulas, we can find out the remaining three.The relation between the remaining three identities are :
sin ? = 1 / cosec ?
tan ? = 1 / cot ?
cos ? = 1 / sec ?
The other three relations are inversely proportional to each other.
In addition, we should be aware of some more formulas like :
(a) sin (A + B) = sin A cos B + cos A sin B
(b) sin (A - B) = sin A cos B - cos A sin B
(b) cos (A + B) = cos A cos B - sin A sin B
(d) cos (A - B) = cos A cos B + sin A sin B
The various value for the above trigonometrical identities are as shown in the table below:
| 00 | 300 | 450 | 600 | 900 | |
| sin ? | 0 | 1 / 2 | 1 / ?2 | ?3 / 2 | 1 |
| cos ? | 1 | ?3 / 2 | 1 / ?2 | 1 / 2 | 0 |
| tan ? | 0 | 1 / ?3 | 1 | ?3 | ? |
| cosec ? | ? | 2 | ?2 | 2 / ?3 | 1 |
| sec ? | 1 | 2 / ?3 | ?2 | ?2 | ? |
| cot ? | ? | ?3 | 1 | 1 / ?3 | 0 |
With the help of above trigonometrical values we can solve any trigonometrical identity question. We need to go through the complete table, so that there is no problem in solving questions in the near future.
In addition to this, we need to remember some more values which are as follows :
(a) sin 10 = 0.0175
(b) cos 10 = 0.9998
(c) tan 10 = 0.0175
Also, we need to remember some formulas like
(a) sin 2? = 2 sin ? cos ?
(b) cos 2? = 2 cos2 ? - 1
(c) tan 2? = 2 tan ? / (1 - tan2 ?)
(1) It is used in the measurement of the height of the flying aeroplanes.
(2) It can be used for the measurement of depth of the sea water.
(3) It can be used for measuring the length of the ladder.
Problems on trigonometric tables :
(1) Find the value of sin 150?
Sol : We can write sin 150 = sin (450 - 300)
Now, the formula for sin (A - B) = sin A.cos B - cos A.sin B
So, sin 150 = sin (450 - 300) = sin 450.cos 300 - cos 450.sin 300
=> sin 150 = 1 / ?2 . ?3 / 2 - 1 / ?2 . 1 / 2
=> sin 150 = (?3 - 1) / 2?2
(2) Find the value of sin 20?
Sol : We know the value of sin 10 = 0.0175, and cos 10 = 0.9998
Now, sin 2? = 2 sin ? cos ?
=> sin 20 = 2 sin 10 cos 10
=> sin 20 = 2 × 0.0175 × 0.9998
=> sin 20 = 0.034993
In this manner, we can find out the value of any trigonometric function, by knowing the above basic formulas and values.
