Arcsin of √3/2

Arcsin, Arccos, Arctan, Arccot

What is arcsin(√3/2)?

Answer

arcsin(√3/2) =

60° = π/3

Range: arcsin x is an angle from −90° to 90°, so the answer is unique.

arcsin(√3/2) is the angle α in [−90°, 90°] with sin α = √3/2.

α = arcsin(√3/2) = 60°

P(cos 60°, sin 60°) = (1/2, √3/2)

P lies on the line y = √3/2 in the right half of the circle, where cos α ≥ 0; highlighted: sin α = √3/2.

arcsin(√3/2) = 60° = π/3

Look in the table for the angle α in [−90°, 90°] with sin α = √3/2: it is 60°, or π/3 in radians.

The calculator is in radian mode (RAD) and gives the angle in radians: arcsin(√3/2) = π/3 ≈ 1.0472 rad. In degrees (DEG) it is 60°.