engineering mathematics MCQ #5553

If sin(x) = 1/2, then what is the value of cos(x/2)?

engineering mathematics MCQ #5553

  1. Question 1

    Q1. If sin(x) = 1/2, then what is the value of cos(x/2)?

    • A) √3/2
    • B) 1/2
    • C) √(3/4 + 1/4)/√2
    • D) √(3/4 - 1/4)/√2

    Answer: √(3/4 + 1/4)/√2

    Explanation: Using the half angle formula, cos(x/2) = √((1 + cos(x))/2). First, find cos(x) = √(1 - sin²(x)) = √(1 - (1/2)²) = √3/2. Then, cos(x/2) = √((1 + √3/2)/2).