### Home > A2C > Chapter 8 > Lesson 8.2.2 > Problem 8-127

Find an equation for each graph below. Homework Help ✎

Use the general equation *y* = *a* · sin *b*(*x* − *h*) + *k*.

Determine the value for each of the four parameters.

First choose a function (sine or cosine) by identifying a convenient locator point.

In this case, we will use:

Since our point is on the midline, we will use the cosine function.

The *x*-value of the point also represents the horizontal shift:

Next find *k*, the vertical shift.

The graph *y* = sin *x* has a midline at *y* = 0 (the *x*-axis).

The parameter *k* is the distance that midline is shifted vertically.

In this case *k* = 2.

The amplitude (a) is the distance from the midline (*k*) 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.

You will learn more about the parameter *b* in future lessons.

For now, know that *b* = 1 since the distance from the beginning to the end of one cycle is 2π.

See part (a).

Pay careful attention to the scale on the *y*-axis when determining *a* and *k*.

notice the first cycle of the graph is an inverted sine curve, so the *a* value will be negative.

See part (a).

See parts (a) and (c).