Answer:
The numbers [tex]3\pi/2 , 5\pi/2[/tex] satisfy the conclusion of Rolle's Theorem
Step by step.
1. The function must be continuous.
Trigonometric functions are continuous.
2. It must be true that [tex]f(a) = f(b) = 0[/tex]
For this case [tex]sin(\pi) = sin( 3\pi) = 0[/tex]
3. Therefore by Rolle's Theorem, there exist a point [tex]x[/tex] such that [tex]f'(x) = 0[/tex].
For this case [tex]f'(x) = cos(x)[/tex]
And [tex]cos(x) = 0[/tex] at [tex]x = 3\pi/2 , 5\pi/2[/tex]
