The answer is -1/2 but how?

Question

Which of the following is the minimum value of the function f(x)= sinxcosx?
a) 0
b) -1/2
c) -1
d) does not exist

Answer 1

f(x) = sinxcosx
= (1/2) sin (2x) by a common identity

At this point I have my answer.
y = (1/2)sin(2x) has an amplitude of 1/2
that is , its maximum is 1/2 and its minimum is -1/2

Answer 2

thanks!