Chapter 5.2, Problem 84E

DISCOVER ■ PROVE: More Reduction Formulas By the Angle-Side-Angle Theorem from elementary geometry, triangles CDO and AOB in the figure to the right arc 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:

$\begin{array}{c}\begin{array}{cc}\sin \left(t+\frac{\pi }{2}\right)=\cos t& \cos \left(t+\frac{\pi }{2}\right)\end{array}=-\sin t\\ \tan \left(t+\frac{\pi }{2}\right)=-\cot t\end{array}$