Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Values of the Following Trigonometric Ratio: Cos 19 π 4 - Mathematics

Find the values of the following trigonometric ratio:

$\cos\frac{19\pi}{4}$

#### Solution

We have:

$\cos\frac{19\pi}{4} = \cos 855^\circ$

$855^\circ = 90^\circ \times 9 + 45^\circ$

$855^\circ\text{ lies in the second quadrant in which the cosine function is negative . }$

Also, 9 is an odd integer .

$\therefore \cos\left( 855^\circ \right) = \cos\left( 90^\circ \times 9 + 45^\circ \right) = - \sin\left( 45^\circ \right) = - \frac{1}{\sqrt{2}}$

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 1.11 | Page 39