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0=sin((t^(2))/(2))

$0=\sin \left(\frac{t^{2}}{2}\right)$

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Powers with negative bases

Full solution

Q.

0=\sin \left(\frac{t^{2}}{2}\right)

Identify $\sin(0)$ condition: Calculate the value of $\sin\left(\frac{t^2}{2}\right)$ when it equals $0$ . $\newline$ Since $\sin(x) = 0$ for $x = n\pi$ , where $n$ is an integer, we have $\frac{t^2}{2} = n\pi$ .
Solve for $t^2$ : Solve for $t^2$ by multiplying both sides by $2$ . $\newline$ $t^2 = 2n\pi$ .
Find $t$ : Take the square root of both sides to solve for $t$ . $t = \pm\sqrt{2n\pi}.$
Determine possible values for $\newline$ $t$ : Since $n$ is an integer, $t$ can be any multiple of \(\newline\)ackslash sqrt{\(2\)ackslash pi}\( or \)-ackslash sqrt{\(2\)ackslash pi}.

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