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在中学数学课本中,总是把半角公式表示为sinα/2=±((1-cosα)/2)~(1/2),cosα/2=±((1+cosα)/2), tgα/2=±((1-cosα)/(1+cosα))~(1/2)然后再补充说明正负号的选取方式。有些课本还进一步说明:若不知α角所在的象限,则应保留其±号。我们知道,在数学里,类似x=±3~(1/2)的式子表示多值.如方程x~2=3的解为x=±3~(1/2),表示不管在什么情况下,3~(1/2)与-3~(1/2)都是方程的解。而半角的正弦、余弦、正切值是单值的,所以,尽管有了正负号选取的补充说明,半角公式采用上述多值表达式还是不恰当的。
In middle school math textbooks, the half-width formula is always expressed as sinα/2=±((1-cosα)/2)~(1/2), cosα/2=±((1+cosα)/2), tgα /2=±((1-cosα)/(1+cosα))~(1/2) Then add the selection method of the sign. Some textbooks further explain that if you do not know the quadrant in which the alpha angle is located, you should retain its number. We know that in mathematics, a formula like x=±3~(1/2) represents multiple values. If the solution of the equation x~2=3 is x=±3~(1/2), it means that no matter what Under the circumstances, 3~(1/2) and -3~(1/2) are solutions of the equation. The sine, cosine, and tangent of the half-angle are single-valued. Therefore, despite the supplementary explanation of sign selection, it is not appropriate to use the above multi-valued expression.