Question

In triangle ABC, right angled at B, if $\angle$A is made larger and larger till it becomes ${90}^{\circ }$, find the value of Sin A and Cos A.

• A. 0, 1
• B. 1, 1
• C. 1, 0
• D. 0 ,0

Answer 1

The correct option is C

1, 0

$\angle$A gets larger and larger in the $△$ABC till it becomes ${90}^{\circ }$. As $\angle$A becomes larger and larger, $\angle$C gets smaller and smaller. The length of the side AB goes on decreasing. The point A gets closer to point B and finally $\angle$A becomes very close to ${90}^{\circ }$. $\angle$C becomes very close to $0^{\circ }$ and the side AC becomes almost coincide the side BC.

When $\angle$C is very close to zero, $\angle$A is very close to ${90}^{\circ }$, The side AC is nearly the same as side BC and AB is close to zero, and the value of Sin A = $\frac{BC}{AC}$ is very close to 1 and the value of cos A = $\frac{AB}{AC}$ which is zero

so, when A = ${90}^{\circ }$, we define sin ${90}^{\circ }$ = 1

cos A = cos ${90}^{\circ }$ = 0