Inverse Sine (Arcsin) Calculator
Calculate the inverse sine (arcsin) of a value. Returns the angle whose sine equals the input.
Angle Rad
0.52359878
Formula
## Inverse Sine (Arcsin) ### Definition **arcsin(x) = the angle whose sine is x** If sin(angle) = x, then arcsin(x) = angle. ### Domain and Range - **Domain**: -1 ≤ x ≤ 1 - **Range**: -90° to 90° (-pi/2 to pi/2 radians) ### Common Values - arcsin(0) = 0° - arcsin(0.5) = 30° - arcsin(√2/2) = 45° - arcsin(1) = 90°
Exemplo Resolvido
Find arcsin(0.5).
- 01arcsin(0.5) = pi/6 radians
- 02= 30 degrees
- 03Verification: sin(30°) = 0.5
Perguntas Frequentes
What is arcsin?
Arcsin (inverse sine) returns the angle whose sine equals the given value. It undoes the sine function.
Why is the range limited to -90° to 90°?
To make arcsin a proper function (single output), its range is restricted to -90° to 90°. Other angles with the same sine can be found using symmetry.
What happens if the input is outside -1 to 1?
Arcsin is only defined for inputs between -1 and 1 in real numbers, since sine never produces values outside this range.
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