what is the value of sin4x value?

Answer 1

Let f(x) = sin(4x)

Apply derivative each side.

f'(x) = cos(4x)(4)                    [anti derivative of 4x is 4]

So, f'(x) = 4cos(4x)

Now, you make f'(x) = 0

4cos(4x) = 0

Divide each side by 4, then cos(4x) = 0.

4x = arc cos(0) ⇒ 4x = 90 = π/2

Divide each side by 4. then x = π/8

If x= π/8 then f(π/8) = sin(4π/8) = sin(π/2) = 1

Therefore sin(4x) = 1.