f(0) = 0
f(0.5pi) = 1
f(pi) = 0
f(1.5pi) = -1
f(2pi) = 0
f'(0.5pi) = 0
f'(1.5pi) = 0
f'(0) = sin'(0)
f'(pi) = sin'(pi)
f'(2pi) = sin'(2pi)
f''(0) = sin''(0)
f''(0.5pi) = sin''(0.5pi)
f''(pi) = sin''(pi)
f''(1.5pi) = sin''(1.5pi)
f''(2pi) = sin''(2pi)
f'''(0) = sin'''(0)
f'''(2/3pi) = sin'''(2/3pi)
f'''(4/3pi) = sin'''(4/3pi)
f'''(2pi) = sin'''(2pi)
f(0.5) = sin(0.5)
f(2pi - 0.5) = sin(2pi - 0.5)
f'(0.5) = sin'(0.5)
f'(2pi - 0.5) = sin'(2pi - 0.5)
f''(2pi - 0.5) = sin''(2pi - 0.5)
f(-pi) = 0
f(3pi) = 0
f(4pi) = 0