“Law of Cosines”的概念、定义、习题解题方法及翻译-数学辞典

单词

Law of Cosines

释义

Law of Cosines

Let , , and be the lengths of the legs of a Triangle opposite Angles , , and . Then the law of cosines states

(1)

This law can be derived in a number of ways. The definition of the Dot Product incorporates the lawof cosines, so that the length of the Vector from

is given by

			(2)
			(3)
			(4)

where

is the Angle between

and

The formula can also be derived using a little geometry and simple algebra. From the above diagram,



			(5)

The law of cosines for the sides of a Spherical Triangle states that

			(6)
			(7)
			(8)

(Beyer 1987). The law of cosines for the angles of a Spherical Triangle states that

			(9)
			(10)
			(11)

(Beyer 1987).

See also Law of Sines, Law of Tangents

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 79, 1972.

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 148-149, 1987.

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