Arcsin of 0

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arcsin(0)?

Answer

arcsin(0) =
0° = 0

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

arcsin(0) is the angle α in [−90°, 90°] with sin α = 0.

sin 0° = 0 ✓

xyOP

α = arcsin(0) = 0°

P(cos 0°, sin 0°) = (1, 0)

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

All four inverse functions of 0
FunctionDegreesRadians
arcsin(0)0°0
arccos(0)90°π/2
arctan(0)0°0
arccot(0)90°π/2

See Also

Recalculate with different values ↑

Arcsine of nearby values

xarcsin x
−√2/2−45° = −π/4
−1/2−30° = −π/6
−0.3≈ −17.4576°
00° = 0
0.1≈ 5.7392°
1/5≈ 11.5370°
1/4≈ 14.4775°

FAQ

What is arcsin(0)?

arcsin(0) = 0° = 0

How to find arcsin(0) from a table of sines?

Look in the table for the angle α in [−90°, 90°] with sin α = 0: it is 0°, or 0 in radians.

What is the difference between arcsin, sin⁻¹ and 1/sin?

sin⁻¹ x is another way to write arcsin x (that is how the calculator key is labelled), not 1/sin x: 1/sin x is the cosecant. arcsin x is the angle whose sine is x; it exists only for −1 ≤ x ≤ 1. Here: arcsin(0) = 0° = 0.

See Also