Periodicity identities allow shifting angles by \boldsymbol{\frac{\pi}{2}}, \boldsymbol{\pi}, \boldsymbol{2\pi}, etc.:

\boldsymbol{\sin\left(\frac{\pi}{2} - \theta\right) = \cos \theta}
\boldsymbol{\cos\left(\frac{\pi}{2} - \theta\right) = \sin \theta}
\boldsymbol{\sin(\pi + \theta) = -\sin \theta}
\boldsymbol{\cos(\pi + \theta) = -\cos \theta}