Question

Find the value of the following trigonometric ratio :

\[ \tan \frac{7\pi}{4} \]

Solution

\[ \tan \frac{7\pi}{4} = \tan\left(2\pi-\frac{\pi}{4}\right) \]

Using,

\[ \tan(2\pi-\theta)=-\tan\theta \]

\[ = -\tan\frac{\pi}{4} \]

\[ = -1 \]

Answer :

\[ \boxed{ \tan\frac{7\pi}{4}=-1 } \]