I can describe how it would look and provide you with the information needed to sketch it yourself.

Given the continuous signal x(t) = cos(2π10000t), you're asked to sketch the first 0.5 ms (milliseconds) of x(t). To do this, you'll need to label the axes and determine the aliased frequency f.

Labeling the axes and ticks:
The x-axis represents time (t) and should be labeled "time (t) in ms."
The y-axis represents the amplitude of the signal and should be labeled "Amplitude."

For the time range of 0 to 0.5 ms, you can create tick marks at intervals such as 0.1 ms, which would give you 5 equally spaced ticks (0, 0.1, 0.2, 0.3, and 0.4 ms). The amplitude of a cosine function varies between -1 and 1, so you can label the y-axis accordingly.

Sketching x(t):
The signal x(t) is a cosine function with a frequency of 10000 Hz or 10 kHz. Within the given time range (0 to 0.5 ms), you can calculate how many periods of the cosine wave will fit:

Period (T) = 1 / frequency = 1 / 10000 = 100 μs (microseconds)

Since 0.5 ms equals 500 μs, there will be 5 complete periods of the cosine wave in the given time range. Sketch a cosine function starting from the amplitude of 1, moving to 0, then -1, back to 0, and reaching 1 again, repeating this pattern 5 times within the 0.5 ms time range.

Aliased frequency (f):
To determine the aliased frequency, you'll need to know the sampling rate used. Aliasing occurs when the sampling rate is less than twice the highest frequency present in the signal, according to the Nyquist-Shannon sampling theorem. Please provide the sampling rate to calculate the aliased frequency.

I hope this description helped you with the sketch.
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