Arcsin of √2/2

Arcsin, Arccos, Arctan, Arccot

What is arcsin(√2/2)?

Answer

arcsin(√2/2) =

45° = π/4

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

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

α = arcsin(√2/2) = 45°

P(cos 45°, sin 45°) = (√2/2, √2/2)

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

arcsin(√2/2) = 45° = π/4

Look in the table for the angle α in [−90°, 90°] with sin α = √2/2: it is 45°, or π/4 in radians.

The calculator is in radian mode (RAD) and gives the angle in radians: arcsin(√2/2) = π/4 ≈ 0.7854 rad. In degrees (DEG) it is 45°.