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 ?

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 ?

anonymous · Answer

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

anonymous · Answer

and (-y)^2 = y^2

anonymous · Answer

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

fifciol · Answer

what does f(x) look like?
It's something like that:|dw:1374336896596:dw|
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