A signal x(n) having z-transform, X(z) = sin z. The value of signal x(n) at n = - 5 can be given as $\frac{1}{A}$ . Then the value of A is_______
120

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Solution

The correct option is A 120
We know that, $s i n (x) = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} + . . . .$

$X (z) = s i n z = z - \frac{z^{3}}{3!} + \frac{z^{5}}{5!} - \frac{z^{7}}{7!} + . . . .$

$x (- 5) = \frac{1}{5!} = \frac{1}{A}$

$A = 5! = 120$

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