SOLUTION: For the sinusoidal function below, give its vertical shift, amplitude, phase shift, period, and range. The, graph two periods of the function, labeling five consecutive key points

Algebra ->  Trigonometry-basics -> SOLUTION: For the sinusoidal function below, give its vertical shift, amplitude, phase shift, period, and range. The, graph two periods of the function, labeling five consecutive key points      Log On


   

Question 1078936: For the sinusoidal function below, give its vertical shift, amplitude, phase shift, period, and range. The, graph two periods of the function, labeling five consecutive key points.
y= -cos(x/4-π/2)
Can someone help me to solve this?
Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Definitions:
y = A cos(Bx + C) + D
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amplitude = A
period = 2π/B
phase shift = −C/B
vertical shift = D
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+y+=+-cos%28+x%2F4+-+pi%2F2+%29+
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+D+=+0+
so, the vertical shift is +0+
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+A+=+-1+
so, the amplitude is +-1+
( same as the regular amplitude, except inverted )
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+-C%2FB+=+%28-%28-pi%2F2%29%29%2F%281%2F4%29+
+-C%2FB+=+4%2A%28pi%2F2%29+
+-C%2FB+=+2%2Api+
So, the phase shift is +2%2Api+, which is 360 degrees,
which means there is no phase shift at all.
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+%282%2Api%29%2FB+=+%282%2Api%29%2F%281%2F4%29+
+%282%2Api%29%2FB+=+8%2Api+
so, the period is +8%2Api+
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The range is from +-1+ to +%2B1+ which is +2+
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Here is the plot over 2 periods, or +16%2Api+
+graph%28+400%2C+400%2C+-30%2C+30%2C+-2%2C+2%2C+-cos%28+x%2F4+-+pi%2F2+%29+%29+
( note that a period of +8%2Api+=+25.13+
which is about what I see on the plot )