sin(5x)/sin(4x) = ?
How do I cancel them out to get a constant?
4 answers
sin(5x)=sin(4x+x)=2sin4xsinx
what property is this? in terms of a and b?
not true Bob,
sin(4x+x)sin4x = (sin4xcosx + cos4xsinx)sin4x
= cosx + cos4xsinx/sin4x
now sin4x = sin(3x+x) = sin3xcosx + cos3xsinx
and cos4x = cos3xcosx - sin3xsinx)
now in your list of trig expansions you might have seen:
sin3x = 3sinx - 4sin^3 x
cos3x = 4cos^3 x - 3cosx
now if you have the patience to plug all that back into the above, you will have a great mess
but all expressed in x.
Don't really know what you wanted here.
sin(4x+x)sin4x = (sin4xcosx + cos4xsinx)sin4x
= cosx + cos4xsinx/sin4x
now sin4x = sin(3x+x) = sin3xcosx + cos3xsinx
and cos4x = cos3xcosx - sin3xsinx)
now in your list of trig expansions you might have seen:
sin3x = 3sinx - 4sin^3 x
cos3x = 4cos^3 x - 3cosx
now if you have the patience to plug all that back into the above, you will have a great mess
but all expressed in x.
Don't really know what you wanted here.
sin(4x+x)sin4x = (sin4xcosx + cos4xsinx)sin4x
should have been:
sin(4x+x) / sin4x = (sin4xcosx + cos4xsinx) / sin4x
should have been:
sin(4x+x) / sin4x = (sin4xcosx + cos4xsinx) / sin4x