Arcsin of 1/2

Arcsin, Arccos, Arctan, Arccot

What is arcsin(1/2)?

Answer

arcsin(1/2) =

30° = π/6

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

1/2 = 0.5.

arcsin(1/2) is the angle α in [−90°, 90°] with sin α = 1/2.

α = arcsin(1/2) = 30°

P(cos 30°, sin 30°) = (√3/2, 1/2)

P lies on the line y = 1/2 in the right half of the circle, where cos α ≥ 0; highlighted: sin α = 1/2.

arcsin(1/2) = 30° = π/6

Look in the table for the angle α in [−90°, 90°] with sin α = 1/2: it is 30°, or π/6 in radians.

The calculator is in radian mode (RAD) and gives the angle in radians: arcsin(1/2) = π/6 ≈ 0.5236 rad. In degrees (DEG) it is 30°.