Question

In $\Delta$ABC, right angled at B, if $\angle A$ is made smaller and smaller till it becomes zero, find the value of sin A and cos A.

• A. 0, 1
• B. 0, $\sqrt{3}$
• C. 0, Not defined
• D. Not defined, 0

Answer 1

The correct option is A

0, 1

$\angle A$ gets smaller and smaller and the length of the side BC decreases. The point C gets closer to point B and finally $\angle A$ becomes very close to zero. AC becomes almost the same as AB.

When BC gets very close to zero, the value of sin A = $\frac{BC}{AC}$ is very close to zero

and AC becomes equal to AB which makes cos A = $\frac{AB}{AC}$ becomes close to 1

So, when A = $0^{\circ }$, we define $sinA=sin{0}^{\circ }$ = 0

$cosA=cos{0}^{\circ }$ = 1

With sin and cos ratios of $0^{\circ }$ known, other ratios can be easily determined.