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From: William Elliot on 30 Jul 2010 00:56 What are the solutions to the equations sin^-1 x = 1/sin x, cos^-1 x = 1/cos x? Since sin^-2 x = 1/sin^2 x, x can be anything not in pi.Z. Since cos^-2 x = 1/cos^2 x? x can be anything not in pi(Z + 1/2).
From: Henry on 30 Jul 2010 11:08 On 30 July, 05:56, William Elliot <ma...(a)rdrop.remove.com> wrote: > What are the solutions to the equations > > sin^-1 x = 1/sin x, If "sin^-1 x" means arcsin(x) then there are real solutions of about +/- 0.944039.
From: Ray Vickson on 30 Jul 2010 12:02 On Jul 29, 9:56 pm, William Elliot <ma...(a)rdrop.remove.com> wrote: > What are the solutions to the equations > > sin^-1 x = 1/sin x, > > cos^-1 x = 1/cos x? > > Since > sin^-2 x = 1/sin^2 x, If sin^-1 x means arcsin(x), then what the heck does sin^-2 x mean? Is it arcsin(arcsin(x))? R.G. Vickson > x can be anything not in pi.Z. > > Since > cos^-2 x = 1/cos^2 x? > x can be anything not in pi(Z + 1/2).
From: William Elliot on 31 Jul 2010 03:42 On Fri, 30 Jul 2010, Ray Vickson wrote: > On Jul 29, 9:56�pm, William Elliot <ma...(a)rdrop.remove.com> wrote: >> What are the solutions to the equations >> >> sin^-1 x = 1/sin x, >> >> cos^-1 x = 1/cos x? >> >> Since >> sin^-2 x = 1/sin^2 x, > > If sin^-1 x means arcsin(x), then what the heck does sin^-2 x mean? Is > it arcsin(arcsin(x))? > Does sin^2 x = sin sin x? >> x can be anything not in pi.Z. >> >> Since >> cos^-2 x = 1/cos^2 x? >> x can be anything not in pi(Z + 1/2). > >
From: Ray Vickson on 31 Jul 2010 17:59
On Jul 31, 12:42 am, William Elliot <ma...(a)rdrop.remove.com> wrote: > On Fri, 30 Jul 2010, Ray Vickson wrote: > > On Jul 29, 9:56 pm, William Elliot <ma...(a)rdrop.remove.com> wrote: > >> What are the solutions to the equations > > >> sin^-1 x = 1/sin x, > > >> cos^-1 x = 1/cos x? > > >> Since > >> sin^-2 x = 1/sin^2 x, > > > If sin^-1 x means arcsin(x), then what the heck does sin^-2 x mean? Is > > it arcsin(arcsin(x))? > > Does sin^2 x = sin sin x? No, but that is not the issue: YOU used the notation sin^-2 x, not me. Why can't you just say what you mean? Is that so hard? R.G. Vickson > > >> x can be anything not in pi.Z. > > >> Since > >> cos^-2 x = 1/cos^2 x? > >> x can be anything not in pi(Z + 1/2). > > |