Correct Answer - Option 2 :
\(\rm sin\ \left(\frac{5\pi}{4}\right)\)
Concept:
sin (2π + x) = sin x ----(1)
Explanation:
\(\rm sin\ \left(\frac{13π}{4}\right)\)
Remove full rotations of 2π until the angle is between 0 and 2π
\(⇒ sin \left ( \frac{13\pi }{4} \right )= sin\left ( \frac{5\pi }{4}+2\pi \right )\)
\(\Rightarrow\rm sin\ \left(\frac{5π}{4}\right)\) [using (1)]
Hence, The value of \(\rm sin\ \left(\frac{13\pi}{4}\right)\) is the same as the value of \(\rm sin\ \left(\frac{5\pi}{4}\right)\).
