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根据正弦值求对应角度(反正弦/arcsin)。

Value (-1 to 1)

Angle Rad

0.52359878

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公式

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°

计算示例

Find arcsin(0.5).

01arcsin(0.5) = pi/6 radians
02= 30 degrees
03Verification: sin(30°) = 0.5

常见问题

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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