Question

If tan theta = 3, theta lies in the third quadrant the value of sec theta is

Answer 1

-$\sqrt{10}$

Answer 2

Answer:

$\sec\theta=-\sqrt{10}$

Step-by-step explanation:

We know the relation

$\sec^2\theta=1+\tan^2\theta\\\\\sec\theta=\pm \sqrt{1+\tan^2\theta}$

Now, we have been given that theta lies in quadrant III. Hence, sec theta will be negative. Thus, we have

$\sec\theta=-\sqrt{1+\tan^2\theta}\\\\\sec\theta=-\sqrt{1+3^2}\\\\\sec\theta=-\sqrt{10}$

The value of sec theta is given by

$\sec\theta=-\sqrt{10}$