The equation sin x + sin y + sin z = -3 for 0 | vedclass

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(A) The range of the sine function is $[-1, 1]$.For the sum $\sin x + \sin y + \sin z$ to be equal to $-3$,each individual term must be equal to its m

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(A) The range of the sine function is $[-1, 1]$.For the sum $\sin x + \sin y + \sin z$ to be equal to $-3$,each individual term must be equal to its minimum value.Therefore,$\sin x = -1$,$\sin y = -1$,and $\sin z = -1$.In the interval $[0, 2\pi]$,the equation $\sin 	heta = -1$ has only one solution,which is $	heta = \frac{3\pi}{2}$.Thus,the only solution set is $(x, y, z) = (\frac{3\pi}{2}, \frac{3\pi}{2}, \frac{3\pi}{2})$.Hence,there is only one solution.

The equation $\sin x + \sin y + \sin z = -3$ for $0 \le x \le 2\pi, 0 \le y \le 2\pi, 0 \le z \le 2\pi$ has:

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