Question

If $\tan \Theta =\frac{1}{\sqrt{5}}and\Theta$ lies in the first quadrant then uthe value of $\cos \Theta$ is

• A. $\frac{1}{\sqrt{6}}$
• B. $-\frac{1}{\sqrt{6}}$
• C. $-\frac{5}{\sqrt{6}}$
• D. $\frac{5}{\sqrt{6}}$

Answer 1

Answer: (D)

$\frac{5}{\sqrt{6}}$

$tan\theta =\frac{1}{\sqrt{5}}=\frac{p}{b}$
and $cos\theta =\frac{b}{h}$
Using Pythagoras, we have
$h=\sqrt{1+5}=\sqrt{6}$
$\therefore cos\theta =\frac{\sqrt{5}}{\sqrt{6}}$