Question

if \[f:\mathbb{R} \rightarrow \mathbb{R}\] with \[ f(x) :=(sin(x))^{2}\].Then its \[\forall x \in \mathbb{R}: f(x) = f(x+\pi)\]. TRUE OR FALSE ?

Answer 1

sin(x+Pi) =-sin(x)

Answer 2

and (-y)^2 = y^2

Answer 3

true cos when you square
(-sin x)^2=(sinx)^2

Answer 4

what does f(x) look like?
It's something like that:
What is the period? Well, for sinx it is 2pi but if you have sin^2x all the negative values become positive values and the period becomes shorter by an amount of 2 so the statement is true