CPM Homework Help : PC Problem 7-127

The graph of a transformation of $y = \cos x$ has the $y$ -axis as a line of symmetry and $\left(20, 50\right)$ as a point of symmetry. The line $y = 15$ is tangent to the graph at many places. Find a possible equation.

Hint:

Since $\left(20, 50\right)$ is a point of symmetry, it is a point of rotational symmetry and must be on the midline.
Since the $y$ -axis is a line of symmetry, the point $\left(−20, 50\right)$ must also lie on the curve.

More Help:

Since $\left(20, 50\right)$ is on the midline, the line $y = 15$ must be a lower boundary line.
Use this information to determine the amplitude and make a possible sketch.

Possible Sketch:

Periodic curve with 3 visible turning points, at (negative 40, comma 15), (0, comma 85), & 40, comma 15), dashed horizontal lines at y = 15, y = 50, & y = 85, highlighted points on curve & center line at (negative 20, comma 50), & (20, comma 50).