Question

Sin(506π+π\4)

Answer 1

\frac{1}{\sqrt{2}}

Answer 2

The sine function has a period of $2\pi$, which means $\sin(x + 2n\pi) = \sin(x)$ for any integer $n$. Since $506\pi = 2 \times 253 \pi$, we can simplify the expression: $\sin(506\pi + \frac{\pi}{4}) = \sin(\frac{\pi}{4})$. The value of $\sin(\frac{\pi}{4})$ is $\frac{1}{\sqrt{2}}$.