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单词 radian
释义

radian

In elementary work, angles are measured in degrees. In more advanced work, particularly involving calculus, it is essential that angles are measured in radians. For example the differential of sine is cosine only when radians are used.

Suppose that a circle of radius 1 with centre O meets two half-lines from O to A and B. Then the size of ∠AOB, measured in radians, equals the length of the arc AB.

On a unit circle, the arc AB equals ∠AOB in radians

1 radian is approximately 57°. More accurately, 1 radian≈57.296°≈57° 17′45″. Since the circumference of a unit circle is 2π, one revolution or 360° measures 2π radians. Consequently, x° = πx/180 radians.

The radian is the SI unit for measuring angle.

Compare steradian.

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更新时间:2025/4/29 16:03:26