How to find arccsc of the square root of two?
Is it possible? Is it in the necessary domain? Any help would be greatly appreciated!
2007-05-13 16:23:05 · 3 answers · asked by DavidEv2 1 in Science & Mathematics ➔ Mathematics
Yes, it's the same as arcsin (√2/2) = π/4
2007-05-13 16:26:19 · answer #1 · answered by Kathleen K 7 · 0⤊ 0⤋
Suppose arccsc â2 = x.
Then by definition csc x = â2
<=> 1 / sin x = â2
<=> sin x = 1/â2
<=> x = Ï/4 + 2kÏ or 3Ï/4 + 2kÏ, for k â Z.
By convention we take [-Ï/2, Ï/2] as the codomain of arccsc, so arccsc â2 = Ï/4.
2007-05-13 23:29:40 · answer #2 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
This is cos^(-1) (â2) , the angle whose cosine is â2.
There is no such angle.
However if it was cos^(-1)(1 / â2) :-
Answer would be 45° and 315°
2007-05-14 04:31:29 · answer #3 · answered by Como 7 · 0⤊ 0⤋