Question

If cos x= √2/2 and x is a fourth quadrant angle, evaluate tan 2x

Answer 1

Since x is a fourth quadrant angle, it is between 270° and 360° (or between -90° and 0°).

So, calculating x, we have:

$\begin{gathered} \cos (x)=\frac{\sqrt[]{2}}{2} \\ x=\cos ^{-1}(\frac{\sqrt[]{2}}{2}) \\ x=-45\degree \end{gathered}$

Now, multiplying x by 2, we have -45 * 2 = -90°.

So the tangent of 2x is:

$\begin{gathered} \sin (-90\degree)=-1 \\ \cos (-90\degree)=0 \\ \tan (-90\degree)=\frac{\sin (-90\degree)}{\cos (-90\degree)}=\frac{-1}{0}=\text{ undefined} \end{gathered}$

Therefore tan 2x is undefined.