To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median. The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.

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5 0

4 years ago

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Find A and B if sin2xcos3x = A sin 5x + B sin x

patriot [66]

Recall that

$\sin(x+y)=\sin x\cos y+\cos x\sin y$
$\sin(x-y)=\sin x\cos y-\cos x\sin y$

Adding these together, you have

$\sin(x+y)+\sin(x-y)=2\sin x\cos y$
$\dfrac12\sin(x+y)+\dfrac12\sin(x-y)=\sin x\cos y$

Replace $x$ with $2x$ and $y$ with $3x$ . You end up with

$\dfrac12\sin(2x+3x)+\dfrac12\sin(2x-3x)=\sin2x\cos3x$
$\sin2x\cos3x=\dfrac12\sin5x+\dfrac12\sin(-x)=\dfrac12\sin5x-\dfrac12\sin x$

and so $A=\dfrac12$ and $B=-\dfrac12$ .

7 0

3 years ago