The exact real value of arcsin(√3/2) is π/3 radians or 60°.
To understand why this is the case, let’s recall that the arcsin function, also known as the inverse sine function, is defined as the angle whose sine is a given number. In this scenario, we are looking for an angle whose sine value equals √3/2.
From basic trigonometry, we know that sin(60°) = √3/2. Therefore, when we take the arcsin of √3/2, we are effectively asking: “What angle gives us a sine of √3/2?” The answer to this inquiry is 60° or, in radians, π/3.
Thus, the exact real value of arcsin(√3/2) is π/3.