Question

If $tan\theta =-\frac{1}{\sqrt{5}}$ and $\theta$ lies in the IV quadrant, then the value of $cos\theta$ is

• A. $\frac{\sqrt{5}}{\sqrt{6}}$
• B. $\frac{2}{\sqrt{6}}$
• C. $\frac{1}{2}$
• D. $\frac{1}{\sqrt{6}}$

Answer 1

The correct option is A

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

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

In the fourth quadrant, $cos\theta$ and $sec\theta$ are positive.

$cos\theta =\frac{1}{sec\theta }$

$=\frac{1}{\sqrt{se{c}^2\theta }}$

$=\frac{1}{\sqrt{1+ta{n}^2\theta }}$

$=\frac{1}{\sqrt{1+(-\frac{1}{\sqrt{5}}{)}^2}}$

$=\frac{1}{\sqrt{\frac{6}{5}}}$

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