What is the smallest positive value for x where y = sin 2x reaches its maximum?

Solution:

Given, y = sin 2x

We have to find the smallest positive value for x where y = sin 2x reaches its maximum.

sin(2x) is always between -1 and 1.

Since sin(π/2) is the first time that it reaches 1,

sin(2x) = 1

When 2x = π/2

So, x = π/2(2)

x = π/4

In other words, the amplitude of sin(x) is 1, so we want

sin(2x) = 1

Taking inverse of sin, we get,

2x = π/2

Dividing by 2 on both sides,

x = π/4

Therefore, the smallest possible value of x is π/4.

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What is the smallest positive value for x where y = sin 2x reaches its maximum?

Summary:

The smallest positive value for x where y = sin 2x reaches its maximum is π/4.