推 unixxxx : arctan(x/y) + arctan(y/x) = π/2 我在書上有看到 02/15 14:49
→ unixxxx : 欸 要怎麼證明@@ 02/15 14:49
推 wayne2011 : Let alpha=arctan(x/y),beta=arctan(y/x),最後和角. 02/15 14:54
正確的恆等式應該是
arctan(x) + arccot(x) = π/2
當x/y > 0
arccot(y/x) 和 arctan(y/x) 互為餘角
=> arccot(y/x) + arctan(y/x) = π/2
當y/x < 0
arctan(y/x) = -arctan(|y/x|)
arccot(|y/x|) + arccot(y/x) = π
=> -arctan(y/x) + π - arccot(y/x) = π/2
=> arctan(y/x) + arccot(y/x) = π/2
所以arctan(y/x) + arccot(y/x) = π/2得證
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推 unixxxx : 為什麼arccot(|y/x|) + arccot(y/x) = π @@ 02/15 17:40
→ Honor1984 : cot[π - 餘角] = -cot[餘角] 02/15 22:51