Understanding trigonometric identities Can someone help me understand trigonometric identities? For example, it is known that $\cos(90-\theta)$ is equal to $\sin \theta$, and vice versa. But why? Is it something to do with the unit circle? Is it visual?

Note that 
\[ \sin(90^{\circ})=1 \]
\[ \cos(90^{\circ})=0 \]
\[ \cos(\alpha - \beta)= \cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)\]
Then
\[
\cos(90^{\circ}-\theta)=\cos(90^{\circ} )\cos(\theta)+\sin(90^{\circ})\sin\theta =0\cdot\cos(\theta)+1\cdot\sin\theta=\sin\theta
\]
