My Math Forum simplify this ?2sin(2x+45°)

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 March 5th, 2014, 07:42 AM #1 Newbie   Joined: Mar 2014 Posts: 28 Thanks: 0 simplify this ?2sin(2x+45°) Hi! I want to simplify this ?2sin(2x+45°), but all I can think of is y=?2sin(2x+45°) and make a graph.. In that case, baseline is 0, ?2 is the amplitude, the period is 180, pitch 45° and starting point is -22.5 (I might have that wrong because 45 is in degrees), the maxline is 1.41 and minimum is -1.41. Is that correct way to do it, or is there another way to simplify it? I really don't understand the question. Best regards.
 March 5th, 2014, 09:57 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,948 Thanks: 1139 Math Focus: Elementary mathematics and beyond Re: simplify this ?2sin(2x+45°) $\sqrt2\sin(2x\,+\,45)\,=\,\sqrt2$$\sin(2x)\cos(45) \,+\,\sin(45)\cos(2x)$$ \\ =\,sqrt2$$\sin(2x)\frac{\sqrt2}{2}\,+\,\frac{\sqrt 2}{2}\cos(2x)$$ \\ =\,\sin(2x)\,+\,\cos(2x)$
 March 5th, 2014, 10:19 AM #3 Newbie   Joined: Mar 2014 Posts: 28 Thanks: 0 Re: simplify this ?2sin(2x+45°) Found the answer.. but it was rather fun to make the graph Thanx
 March 5th, 2014, 12:51 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,757 Thanks: 2138 That's probably the intended answer, but it's debatable whether it's any simpler than the original expression.

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