# What tis the complete domain D and range R of the following multivariable functions: w=2sin xy

Question
Multivariable functions
What tis the complete domain D and range R of the following multivariable functions:
$$\displaystyle{w}={2}{\sin{{x}}}{y}$$

2021-02-01
$$\displaystyle{w}={2}{\sin{{x}}}{y}$$
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, $$\displaystyle{R}={\left[−{2},{2}\right]}$$

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