We have to find the smallest value of x for which y = sin(3x + pi/2) has the maximum value.
The sine function can have a maximum value of 1.
We know that y = sin (3x + pi/2) = 1. The least value of x for which the sine function has a value of 1 is pi/2.
This gives 3x + pi/2 = pi/2
=> 3x = 0
=> x = 0
The function y = sin(3x + pi/2) has the maximum value when x = 0
sin(3x + pi/2) = 13x + pi/2 = arcsin 1
3x + pi/2 = pi/2We'll eliminate pi/2 and we'll get:
3x = 0x = 0
The smallest positive value of x for y = sin(3x + pi/2) is maximum is x = 0.