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What are the maximum and minimum values of the expression sin x cos x?

1. 1/2, -1/2
2. 1/4, -1/4
3. 1/4, -1/4
4. 2, -2

Correct answer: 1/2, -1/2

Solution

sin x cos x = (1/2) sin 2x, and sin 2x ranges from -1 to 1, so the expression ranges from -1/2 to 1/2. Maximum is 1/2 and minimum is -1/2.

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