is very close to °, AC is nearly the same as AB and so the value of cos A = AB AC is very close to . This helps us to see how we can define the values of sin A and cos A when A = °. We define : sin ° = and cos ° = . Using these, we have : tan ° = sin ° cos ° = , cot ° = , tan ° which is not defined.
(Why?) sec ° = cos = and cosec ° = , sin which is again not defined.(Why?) Now, let us see what happens to the trigonometric ratios of A, when it is made larger and larger in ABC till it becomes °. As A gets larger and larger, C gets smaller and smaller. Therefore, as in the case above, the length of the side AB goes on decreasing. The point A gets closer to point B.
Finally when A is very close to °, C becomes very close to ° and the side AC almost coincides with side BC (see Fig. . ). Fig.
. When C is very close to °, A is very close to °, side AC is nearly the same as side BC, and so sin A is very close to . Also when A is very close to °, C is very close to °, and the side AB is nearly zero, so cos A is very close to . So, we define : sin ° = and cos ° = .
Now, why don’t you find the other trigonometric ratios of °? We shall now give the values of all the trigonometric ratios of °, °, °, ° and ° in Table . , for ready reference. Table .
A ° ° ° ° ° tan A Not defined cosec A Not defined sec A Not defined cot A Not defined Remark : From the table above you can observe