What is the smallest positive value of x for which y = sin(3x + pi/2) has a maximum value?  

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The sine function has the maximum value 1, therefore y = 1.

sin(3x + pi/2) = 1

3x + pi/2 = arcsin 1

3x + pi/2 = pi/2

We'll eliminate pi/2 and we'll get:

3x = 0

x = 0

The smallest positive value of x for y = sin(3x + pi/2) is maximum is x = 0.

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