Chapter 13.4, Problem 9OE

To determine

The reason that b in y = sin bx does not affect maximum and minimum value of sine function.

Explanation of Solution

Given:

  $y=\sin bx$

Solution:

The given function.

  $y=\sin bx$ ,

Here, b will affect the curve by horizontal elongation or shrinkage $.$

This will affect the period of the curve. That is why, the maximum and minimum values remains unchanged.

For example,

  $y=a\sin x$

For change in maximum and minimum value, that is vertical elongation or shrinkage occur witch change in value of a. this will affect amplitude of the curve not period.