As we know that the sine functions are continuous and differentiable on R.
Let us find the values of the function f at an extreme
Here, f(-1) = f(0), therefore there exist a c ∈ (-1,0) such that f'(c) = 0.
Let us find the derivative of the function f
As cosine is positive between -π/2 ≤ θ ≤ π/2, for our convenience, we take the interval to be -π/2 ≤ θ ≤ 0, since the value of the cosine repeats.
As we know that 3/π value is nearly equal to 1. Therefore, the value of the c nearly equal to 0.
Therefore, clearly say that c ∈ (-1,0)
Thus, Rolle'* theorem is verified.
