Question:
Mark the tick against the correct answer in the following:
If $\cot ^{-1}\left(\frac{-1}{5}\right)=x$ then $\sin x=?$
A. $\frac{1}{\sqrt{26}}$
B. $\frac{5}{\sqrt{26}}$
C. $\frac{1}{\sqrt{24}}$
D. none of these
Solution:
Given: $\cot ^{-1} \frac{-1}{5}=x$
To Find: The value of $\sin x$
Since, $x=\cot ^{-1} \frac{-1}{5}$
$\Rightarrow \cot x=\frac{-1}{5}=\frac{\text { adjacent side }}{\text { opposite side }}$
By pythagorus theroem,
(Hypotenuse $)^{2}=(\text { opposite side })^{2}+(\text { adjacent side })^{2}$
Therefore, Hypotenuse $=\sqrt{26}$
$\Rightarrow \sin \mathrm{x}=\frac{\text { opposite side }}{\text { hypotenuse }}=\frac{5}{\sqrt{2} 6}$