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What do each of these numbers mean in this equation for sine graphs? y = -3sin[2(x-30)] + 1

I know 1 = shift up What does the rest mean? thanks.

Chris Godsil
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user3293279
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1 Answers1

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3 is the amplitude but it is negative so it reflects the graph about the x axis. The 2 cuts the period by 1/2 because it is computing the inputs twice as fast as normal. The minus 30 means the graph will be shifted right 30 units because to get a point here you have to plug in that point plus 30 to cancel out the 30. And finally the plus 1 shifts the graph up 1 unit.

King Squirrel
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  • What would you have to change on the graph, when the 2 cuts the perioud by 1/2 – user3293279 Apr 30 '14 at 01:54
  • You would multiply every point on the original graph (y=sinx) by 1/2 to get the new points. This is so because the 2 in front of the input makes it so you have to multiply each point by 1/2 first to cancel the 2. So, if this only had the 2 in front of the input and no other translations then it would spit out the sine of pi because it multiplied the pi/2 by 2 before it computed the sine of it. So essentially what happens is the space it takes to complete a period is cut in half because everything is being computed twice as fast as usual. – King Squirrel Apr 30 '14 at 01:57
  • What would the numbers on this graph become? – user3293279 Apr 30 '14 at 01:59
  • That I think you can do!! That's just basic math, just take your time on each point. – King Squirrel Apr 30 '14 at 02:01
  • Do every single numbers change? or just the ones inside the brackets? – user3293279 Apr 30 '14 at 02:02
  • No numbers change in the brackets, it's the numbers on the x axis of the original sine graph that change. – King Squirrel Apr 30 '14 at 02:03
  • I see. What if that number 2 was 3? What would you multiply by? – user3293279 Apr 30 '14 at 02:06
  • Think about it, if something is getting done 3 times as fast it gets done in 1/3 of the time. So it's always 1/#. – King Squirrel Apr 30 '14 at 02:08