Capítulo IV · Neste capítulo você vai
Reduction to the 1st quadrant
- relate $x$ from the 2nd, 3rd and 4th quadrants with $\pi - x$, $x - \pi$ and $2\pi - x$;
- use complementary arcs to reduce everything to the range $\left[0, \frac{\pi}{4}\right]$;
- read a table of values of trigonometric functions;
- extend the reduction formulas to every real $x$;
- recognize even and odd functions and the parity of sine and cosine.
Before calculators, the value of $\operatorname{sen} 251^\circ$ was looked up on a printed tablet. But the boards only had angles from $0^\circ$ to $45^\circ$! The rest was obtained by symmetry: in the cycle, every point has a “twin” in the 1st quadrant, with the same sine and the same cosine, minus the sign. This chapter derives these formulas and shows how the symmetry between $x$ and $-x$ classifies functions into even and odd.
