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# Find the Values of the Following Trigonometric Ratio: Tan ( − 13 π 4 ) - Mathematics

Find the values of the following trigonometric ratio:

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

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#### Solution

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 .
$\therefore \tan \left( - 585^\circ \right) = - \tan \left( 585^\circ \right) = - \tan \left( 90^\circ \times 6 + 45^\circ \right) = - \tan 45^\circ = - 1$

Concept: Negative Function Or Trigonometric Functions of Negative Angles
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 5 Trigonometric Functions
Exercise 5.3 | Q 1.1 | Page 39
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