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Given that 8*sin(theta) = 4 + cos(theta), find sin(theta).

1. 3/5 or 5/13
2. 1/2 or 1/3
3. 4/5 or 12/13
4. 2/5 or 5/13

Correct answer: 3/5 or 5/13

Solution

From cos(theta) = 8s - 4, squaring and using sin² + cos² = 1 gives 65 s² - 64 s + 15 = 0, whose roots are s = 3/5 and s = 5/13.

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