\(\displaystyle{w}={2}{\sin{{x}}}{y}\)

Domain for sine function is real numbers.

Thus, \(\displaystyle{D}=\mathbb{R}{2}\)

Now,\(\displaystyle−{1}\le{\sin{\theta}}\le{1}\)

\(\displaystyle−{1}\le{\sin{{x}}}{y}\le{1}\)

\(\displaystyle−{1}\times{2}\le{2}{\sin{{x}}}{y}\le{1}\times{2}\)

\(\displaystyle−{2}\le{\sin{{x}}}{y}\le{2}\)

So, \(\displaystyle{R}={\left[−{2},{2}\right]}\)

Domain for sine function is real numbers.

Thus, \(\displaystyle{D}=\mathbb{R}{2}\)

Now,\(\displaystyle−{1}\le{\sin{\theta}}\le{1}\)

\(\displaystyle−{1}\le{\sin{{x}}}{y}\le{1}\)

\(\displaystyle−{1}\times{2}\le{2}{\sin{{x}}}{y}\le{1}\times{2}\)

\(\displaystyle−{2}\le{\sin{{x}}}{y}\le{2}\)

So, \(\displaystyle{R}={\left[−{2},{2}\right]}\)