Sine and Cosine are Periodic on Reals/Corollary

Corollary to Sine and Cosine are Periodic on Reals

Let $x \in \R$.

Sign of Cosine on $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$ and $\openint {\dfrac \pi 2} {\dfrac {3 \pi} 2}$

$\cos x$ is strictly positive on the interval $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$ and strictly negative on the interval $\openint {\dfrac \pi 2} {\dfrac {3 \pi} 2}$

Sign of Sine on $\openint 0 \pi$ and $\openint \pi {2 \pi}$

$\sin x$ is strictly positive on the interval $\openint 0 \pi$ and strictly negative on the interval $\openint \pi {2 \pi}$