What is the smallest positive value for x at which y sin 2x attains its maximum?

by

The function y = sin(2x) is periodic and reaches its maximum value at specific points within its cycle. To find the smallest positive value of x where y = sin(2x) reaches its maximum, we first need to identify the properties of the sine function.

The sine function achieves its maximum value of 1 whenever its argument is equal to (2n + 1) rac{
pi}{2}, where n is any integer (0, 1, 2,…). Since we have y = sin(2x), we can set the argument of the sine function as:

2x = (2n + 1) rac{
pi}{2}

To solve for x, we first divide both sides of the equation by 2:

x = rac{(2n + 1) rac{
pi}{2}}{2} = rac{(2n + 1) 
pi}{4}

Now, let’s find the smallest positive value of x by setting n = 0:

x = rac{(2 	imes 0 + 1) 
pi}{4} = rac{
pi}{4}

Thus, the smallest positive value for x at which y = sin(2x) reaches its maximum is:

 x = rac{
pi}{4} 	ext{ radians}

In degrees, this value corresponds to 45^ ext{o}. So, in summary, the smallest positive value for x where y = sin(2x) attains its maximum is rac{
pi}{4} ext{ radians} or 45^ ext{o}.

Leave a Comment