By the "Angle-Side-Angle" theorem from elementary geometry, triangles $C D O$ and $A O B$ in the figure are congruent. Explain how this proves that if $B$ has coordinates $(x, y),$ then $D$ has coordinates $(-y, x) .$ Then explain how the figure shows that the following reduction formulas are valid:
$$\begin{array}{l}{\sin \left(t+\frac{\pi}{2}\right)=\cos t} \\ {\cos \left(t+\frac{\pi}{2}\right)=-\sin t} \\ {\tan \left(t+\frac{\pi}{2}\right)=-\cot t}\end{array}$$
Trigonometric Functions: Unit Circle…
Trigonometric Functions of Real Numbers