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

y = sin 2x

The period of sin 2x = 360/2 = 180
That would make a maximum at x = 45°

(make a sketch to illustrate the answer)

To find the smallest positive value for x where y = sin 2x reaches its maximum, we need to examine the behavior of the function sin 2x.

First, let's understand what sin 2x represents. The 2x inside the sine function refers to the argument of the sine function and can be interpreted as an angle. The value of sin 2x represents the y-coordinate of a point on the unit circle at an angle of 2x.

The sine function oscillates between -1 and 1, with maximum values of 1 occurring at angles where the y-coordinate is at its highest point on the unit circle.

Since we want to find the smallest positive value for x where y = sin 2x is at its maximum, we can conclude that we need to find the smallest positive angle such that the y-coordinate on the unit circle is at its maximum.

To find this angle, we need to understand the period of the function sin 2x. The period of the sine function is 2π, meaning it repeats itself every 2π radians.

Since we are interested in the smallest positive value of x, we can start by setting 2x = 0, which implies x = 0. This gives us the first maximum value of sin 2x.

To find the next maximum value, we need to find the angle that is equivalent to 2π radians added to the initial angle. This can be done by setting 2x = 2π, which implies x = π. So the second maximum value occurs at π.

Since the period of sin 2x is 2π, we can deduce that the maximum values will repeat every 2π radians. Therefore, the smallest positive value for x where y = sin 2x reaches its maximum is x = 0.

In summary, the smallest positive value for x where y = sin 2x reaches its maximum is x = 0, and the maximum values of sin 2x occur at intervals of 2π.