Finding out the frequency of a sine wave

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I have a signal $x[n]$ which has $500$ samples, and I want to generate it such as it consists of two sinusoids added together.

  • The first sinusoid will have an amplitude of $1$, and make $6$ complete cycles in the $500$ samples.
  • The second sinusoid will have an amplitude of $0.5$ and make $44$ complete cycles in the $500$ samples.

Make of plot of this signal.

What I'm not really familiar with is the $6$ complete cycles in $500$ samples part. I assume I should be using $\sin(2\pi f)$? So I should have something like this $$x[n]= \sin(2\pi f) + 0.5 \sin(2\pi f)$$ I know that the periodic time is the time taken to make one complete cycle, so is the $500$ samples considered as the time unit here?

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for first signal: Ts = 500/6=250/3 f=1/T=3/250 now first sin wave=sin((6/250)*πn) you can do same operation for second sin signal so final anwser is x[n]=sin((6/250)*πn)+0.5sin((88/500)*πn)