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October 14th, 2010, 07:01 PM   #1
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Sine

If sin(x-pi)=A sin x, then the number A=___


I don't even know where to start. Please help.
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October 14th, 2010, 07:55 PM   #2
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Re: Sine

sin(x - ?) = A sin(x)

Use the additive angle identity for sine: sin(a ± b) = sin(a)cos(b) ± cos(a)sin(b).

sin(x)cos(?) - cos(x)sin(?)

cos(?) = -1, sin(?) = 0, thus

-sin(x) = A sin(x)

0 = (sin(x))(A + 1)

For sin(x) ? 0,

A = -1
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October 15th, 2010, 06:43 PM   #3
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Re: Sine

Learn the identities below.
sin(A) ? -sin(-A),      cos(A) ? cos(-A),       tan(A) ? -tan(-A)     (if defined)
sin(A) ? sin(? - A),    cos(A) ? -cos(? - A),  tan(A) ? -tan(? - A) (if defined)
sin(A) ? sin(A + 2?), cos(A) ? cos(A + 2?), tan(A) ? tan(A + ?)  (if defined)
They imply that sin(x - ?) ? -sin(? - x) ? -sin(x) ? (-1)sin(x).
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