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Let theta and phi be acute angles with sin(theta) = 1/2 and sin(phi) = 1/3. What is the value of sin(theta + phi)?

1. (2*sqrt(2) + sqrt(3))/6
2. (2*sqrt(2) - sqrt(3))/6
3. (sqrt(3) + sqrt(2))/6
4. (4*sqrt(2) + 7*sqrt(3))/18

Correct answer: (2*sqrt(2) + sqrt(3))/6

Solution

Substituting the sine and cosine values into the sum formula gives sin(theta+phi) = (1/2)(2*sqrt(2)/3) + (sqrt(3)/2)(1/3) = (2*sqrt(2)+sqrt(3))/6.

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