Question

Find the value of the following trigonometric ratio:
\[\tan \frac{7\pi}{4}\]

Answer 1

 We have: 
\[\tan\left( \frac{7\pi}{4} \right) = \tan\left( 315^\circ \right)\]
315° = (90° x 3 + 45°)
\[315^\circ\text{ lies in the fourth quadrant in which the tangent function is nagetive . }\]
Also, 3 is an even integer . 
\[ \therefore \tan\left(  315^\circ \right) = \tan\left( 90^\circ \times 3 + 45^\circ \right) =- \cot45^\circ = -1\]