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Sine graphs



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Tue Feb 26, 2013 7:48 pm
Blues says...



My exam is in two days and our class is extremely disruptive so we never learn anything. This is the exam question:

Image

It's worth three marks - it's a non calculator paper - but I don't know how to work out the answer.

Help would be appreciated! :)
  





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Wed Feb 27, 2013 2:39 am
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Kale says...



My trig is a bit rusty, and I learned to do this with radians, but I'll have a go.

First things first, the lowest and highest points of the graph are 0 and 100. Halfway between these points is the vertical center of your graph, which is 50 in this case. As a result, your offset (or distance from the center of the graph to 0) is 50, which also happens to be your a.

Now that you have a, it's easy to find b. With an offset of 50, the difference between your center and your lowest and highest points is also 50, which happens to also be your b value. Technically, your b value is -50 as the form normally is written as a + bcos(kx), but since there's a minus sign there, I'm guessing that the value wanted is 50.

To find your k, look at the degree where your graph has gone through one whole loop, which is called your period. In this case, the degree happens to be 90*. Normally, a sine wave has a period of 360*. 90 is 1/4 of 360, and so your k value is 1/4.
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Wed Feb 27, 2013 6:34 pm
Blues says...



Thanks Kyll! :D
  








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