Find the maximum, minimum values and minimum positive period of y = b sin ax

Question:

The function y = a sin(1/2)x - b (a > 0) has a maximum value of 4 and minimum value of -2. Find the maximum, minimum value and the minimum positive period of the function y = b sin ax.

Solution:

The maximum value of y = a sin(1/2)x is a. The minimum value of y = a sin(1/2)x is -a. Therefore, from the given condition, we get, a - b = 4 and -a - b = -2. This is a two
variables one-degree equations. By sue the substitution method, we get a = 3 and b= -1. So, the asked function is y = -sin 3x. Therefore, its maximum value is 1, minimum value
is -1 and the minimum positive period is 2pi/3. For a detailed solution, please watch the video.