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If theta is an acute angle satisfying 2 sin(theta) = 2 - cos(theta), what is the value of sin(theta)?

1. 3/5
2. 4/5
3. 1/2
4. 2/3

Correct answer: 3/5

Solution

Substituting cos(theta) = 2 - 2 sin(theta) into the Pythagorean identity yields a quadratic whose acceptable root is sin(theta) = 3/5.

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