Question

Find the values of the following trigonometric ratio:

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

 

Answer 1

We have: 
\[\tan \left( - \frac{13\pi}{4} \right) = \tan \left( - 585^\circ \right)\]
\[\tan \left( - 585^\circ \right) = - \tan \left( 585^\circ \right) = - \tan \left( 90^\circ \times 6 + 45^\circ \right)\]
\[585^\circ\text{ lies in the third quadrant in which tangent function is positive . }\]
Also, 6 is an even integer . 
\[ \therefore \tan \left( - 585^\circ \right) = - \tan \left( 585^\circ \right) = - \tan \left( 90^\circ \times 6 + 45^\circ \right) = - \tan 45^\circ = - 1\]