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Which graph correctly represents y = |sin x| / sin x?

1. A step (square-wave) graph equal to +1 where sin x > 0 and -1 where sin x < 0, undefined at multiples of pi
2. The graph of y = sin x
3. The constant line y = 1 for all x
4. The graph of y = |sin x|

Correct answer: A step (square-wave) graph equal to +1 where sin x > 0 and -1 where sin x < 0, undefined at multiples of pi

Solution

The expression |sin x|/sin x equals the signum of sin x: +1 wherever sin x is positive, -1 wherever it is negative, and undefined at x = n*pi where sin x = 0. The correct graph is the square wave alternating between +1 and -1.

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