What is the value of sin(75 degrees)? (Hard)
Answer and explanation
Correct answer: A. (root 6 + root 2) / 4
- Step 1: Use addition formula sin(45 + 30) = sin 45 cos 30 + cos 45 sin 30. Step 2. (1/root 2)(root 3/2) + (1/root 2)(1/2) = (root 3 + 1) / (2 root 2) = (root 6 + root 2) / 4. Answer: (root 6 + root 2) / 4. Why not the others: (root 6 - root 2)/4 is sin(15 deg); (root 3 + 1)/2 omits denominator factor root 2; 1/2 is sin(30 deg).
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