Question 689126: Find the equation of a sine wave that is obtained by shifting the graph of y=sin(x) to the right 9 units and downward 8 units and is vertically stretched by a factor of 4 when compared to y=sin(x).
Found 2 solutions by stanbon, exodus:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the equation of a sine wave that is obtained by shifting the graph of y=sin(x) to the right 9 units and downward 8 units and is vertically stretched by a factor of 4 when compared to y=sin(x).
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Ans: y = 4sin(x-9)-8
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cheers,
Stan H.
Answer by exodus(1) (Show Source):
You can put this solution on YOUR website! The general equation that should be formed is as follows:
y - A = Bsin(x - C)
where:
A stands for a vertical shift (if A is positive, move is upward; if A is negative, move is downward)
B stands for vertical stretch factor
C stands for a horizontal shift (if C is positive, move is to the right; if C is negative, move is to the left).
We start with the sine wave in 'home' position, having equation y = sin(x) which is really as follows:
y - 0 = 1sin(x - 0)
with
A = 0, (no vertical shift or change)
B = 1, (normal stretch factor or 'amplitude')
C = 0, (no horizontal shift or change)
so, the equation required is as follows:
y - (-8) = 4sin(x - 9)
which can simplify to
y + 8 = 4sin(x - 9)
or, if final equation is given in the form "y in terms of x" (also called 'making y the subject'), then:
y = 4sin(x - 9) - 8
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