. Trigonometric Ratios of ° and ° Let us now calculate the trigonometric ratios of ° and °. Consider an equilateral triangle ABC. Since each angle in an equilateral triangle is °, therefore, A = B = C = °.
Draw the perpendicular AD from A to the side BC (see Fig. . ). Now ABD ACD Therefore, BD = DC and BAD = CAD (CPCT) Now observe that: ABD is a right triangle, right-angled at D with BAD = ° and ABD = ° (see Fig.
Fig. . As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that AB = a .
Then, BD = BC = and AD = AB – BD = ( a ) – ( a ) = a , Therefore, AD = Now, we have : sin ° = BD , cos ° = AD tan ° = BD AD . Also, cosec ° = , sin sec ° = cos cot ° = tan . Similarly, sin ° = AD , cos ° = , tan ° = , cosec ° = , sec ° = and cot ° = Trigonometric Ratios of ° and ° Let us see what happens to the trigonometric ratios of angle A, if it is made smaller and smaller in the right triangle ABC (see Fig. .
), till it becomes zero. As A gets smaller and smaller, the length of the side BC decreases.The point C gets closer to point B, and finally when A becomes very close to °, AC becomes almost the same as AB (see Fig. . ).
When A is very close to °, BC gets very close to and so the value of sin A = BC AC is very close to . Also, when A