What is the value of sin 42 π ?

Choice A is correct. The sine of a number $t$ is the y-coordinate of the point arrived at by traveling a distance of $t$ units counterclockwise around the unit circle from the starting point $\left(1,0\right)$. Since the unit circle has a circumference of $2\pi$ units, it follows that one full rotation around the circle is equal to a distance of $2\pi$ units. Therefore, a distance of $42\pi$ units around the circle from the starting point $\left(1,0\right)$ would result in exactly $21$ full rotations, arriving back at the point $\left(1,0\right)$. So, $\sin 42\pi$ is equal to the y-coordinate of the point $\left(1,0\right)$, which is $0$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the value of $\cos 42\pi$, not $\sin 42\pi$.