### Home > PC > Chapter 6 > Lesson 6.4.1 > Problem 6-141

6-141.

Find a cosine function that has a maximum at (2, 5) and a minimum at (4, 2). Homework Help ✎

Vertical shift: Since the minimum point is at *y* = 2 and the amplitude is 1.5, the vertical shift would be their sum.

Horizontal shift: Since the maximum point is at (2, 5) a cosine function has been shifted 2 units right.

Since a maximum is at *x* = 2 and a minimum is at *x* = 4, half of a cycle is 2 units. Hence, the period is 4.

Use the formula *pb* = 2*π* to calculate *b*.