Question

Find the values of the following trigonometric ratio:

\[\sin\frac{41\pi}{4}\]

Answer 1

 We have: 
\[\sin\frac{41\pi}{4} = \sin 1845^\circ\]
\[1845^\circ = 90^\circ \times 20 + 45^\circ\]
\[1845^\circ\text{ lies in the first quadrant in which the sine function is positive . }\]
Also, 20 is an even integer .
\[ \therefore \sin \left( 1845^\circ \right) = \sin \left( 90^\circ \times 20 + 45^\circ \right) = \sin \left( 45^\circ \right) = \frac{1}{\sqrt{2}}\]