CPM Homework Help : CCA2 Problem 7-129

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7-129.

Find an equation for each graph below.

Hint (a):
Use the general equation $y = a · \sin\left(x − h\right) + k$ .
Determine the value for each of the three parameters.
Step 1(a):
First identify a convenient locator point.
In this case, we will use:
$\left(\frac{\pi}{4}, 2\right)$
The $x-$ value of the point represents the horizontal shift.
The $y-$ value of the point represents the vertical shift.
$h=\frac{\pi}{4},k=2$
Step 2(a):
The amplitude (a) is the distance from the midline $\left(k\right)$ to the highest point.
In this case $k = 2$ and the highest point is $3$ , so $a = 1$ .
Since the graph increases from the locator point in the same way $y = \sin x$ does, a is positive.

Hint (b):
See part (a).
Pay careful attention to the scale on the $y$ -axis when determining $a$ and $k$ .

Hint (c):
If you choose $\left(\frac{\pi}{6},0\right)$ as your locator point, notice the first cycle of the graph is an inverted sine curve, so the a value will be negative.
More Help (c):
See part (a).
Answer (c):
$y=-\sin\left(x-\frac{\pi}{6}\right)+2\text{ or }y=\sin\left(x+\frac{5\pi}{6}\right) +2$

Hint (d):
See parts (a) and (c).

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