Question 388313: Using f(x)=1sin x or f(x)=cos x as a guide,graph each function. Identify the amplitude and the period.
f(x)=2 sin 1/2 x
thnxs
Found 2 solutions by texttutoring, stanbon:
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! The sine graph will look like this: http://www.wolframalpha.com/input/?i=y%3D2+sin(x/2)
(Copy and paste the URL if you can't click it.)
In any sine curve, the general equation is:
y=a*sinb(x-c) + d
Where a=amplitude, b=compression (determines period), c=phase shift (left or right shift), and d=vertical displacement (up/down shift)
In your question, a=2, b=1/2, and c=0, d=0.
So the amplitude is 2. This means that the curve goes up to a max of y=2 and a min of y=-2.
You can find the period by using this simple formula:
P = 2Pi /b
Your value of b is 1/2, so the period is:
P = 2Pi / (1/2)
P = 4Pi
So the period of this function is 4Pi, which you should be able to see from the graph on the link. In essence, this means that the curve was stretched out in the x-direction by double. If b=2, it would be compressed to a period of 1Pi.
Hope this helps!
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Using f(x)= sin x or f(x)= cos x as a guide, graph each function. Identify the amplitude and the period.
f(x)=2 sin 1/2 x
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Period = (2pi)/b = (2pi)/(1/2) = 4pi
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amplitude = |2| = 2
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Cheers,
stan H.
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