SOLUTION: Please help with this calculus problem? I am very stuck on my hw and if someone could please help explain how to find these, so I can have at least one example to work from tha

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Question 910128: Please help with this calculus problem?
I am very stuck on my hw and if someone could please help explain how to find these, so I can have at least one example to work from
thanks so much!

Given the function y = sinx + 5
what is the
a) period
b)amplitude
c) phase shift
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+sin%28x%29+%2B+5 is the same as y+=+1%2Asin%281%2Ax-0%29+%2B+5

Compare y+=+1%2Asin%281%2Ax-0%29+%2B+5 to the general form y+=+A%2Asin%28B%2Ax-C%29+%2B+D

We see that

A = 1
B = 1
C = 0
D = 5

So...

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Amplitude: |A| = |1| = 1

The amplitude is 1

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Period:

T = period

T = 2pi/B

T = 2pi/1

T = 2pi

The period is 2pi

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Phase Shift:

C is the phase shift. Since C = 0, the phase shift is 0. The parent function y = sin(x) has not been moved left or right.

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Midline:

The midline is the center horizontal line that goes through the sine or cosine function.

Since D = 5, the midline is the horizontal line y = 5. Essentially, this means that the y = sin(x) graph has been shifted 5 units up.

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Graph of y+=+sin%28x%29+%2B+5 in red. Midline is the blue dashed horizontal line that cuts through the center of the sine curve.