Question

Find the value of the following trigonometric ratio :

\[ \tan\left(-\frac{13\pi}{4}\right) \]

Solution

\[ \tan\left(-\frac{13\pi}{4}\right) = \tan\left(-\frac{13\pi}{4}+4\pi\right) \]

\[ = \tan\frac{3\pi}{4} \]

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

Using,

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

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

Answer :

\[ \boxed{ \tan\left(-\frac{13\pi}{4}\right)=-1 } \]