Question

Find the value of the following trigonometric ratio :

\[ \sin\left(\frac{41\pi}{4}\right) \]

Solution

\[ \sin\left(\frac{41\pi}{4}\right) = \sin\left(\frac{41\pi}{4}-10\pi\right) \]

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

\[ = \frac{1}{\sqrt2} = \frac{\sqrt2}{2} \]

Answer :

\[ \boxed{ \sin\left(\frac{41\pi}{4}\right) = \frac{\sqrt2}{2} } \]