Capítulo VI · Neste capítulo você vai
Transformations
- demonstrate the formulas for addition and subtraction of arcs for sine, cosine, tangent and cotangent;
- deduce the formulas of the double and triple arcs;
- calculate the functions of $\frac{x}{2}$ from $\cos x$ (division formulas);
- write $\operatorname{sen} x$, $\cos x$ and $\operatorname{tg} x$ in function of $\operatorname{tg}\frac{x}{2}$;
- transform sums into products (Werner and prostapheresis formulas).
Knowing $\operatorname{sen} 30^\circ$ and $\operatorname{sen} 45^\circ$, how much is $\operatorname{sen} 75^\circ$ worth? The formulas in this chapter answer: the functions of a sum of arcs are written with the functions of each arc. All the others come from them — double arc, half arc, products and sums — and with them trigonometry becomes a powerful algebra, used from astronomy to wave physics.
