Capítulo III · Neste capítulo você vai
Fundamental relationships
- demonstrate the relationship $\operatorname{sen}^2 x + \cos^2 x = 1$ using the Pythagorean theorem;
- write tangent, cotangent, secant and cosecant as a function of sine and cosine;
- deduce the relations $1 + \operatorname{tg}^2 x = \sec^2 x$ and $1 + \operatorname{cotg}^2 x = \operatorname{cossec}^2 x$;
- calculate the six circular functions knowing only one of them and the quadrant;
- understand what an identity is and demonstrate it through three methods.
For each $x \ne \dfrac{k\pi}{2}$, chapter II defined six numbers: $\operatorname{sen} x$, $\cos x$, $\operatorname{tg} x$, $\operatorname{cotg} x$, $\sec x$ and $\operatorname{cossec} x$. They are not independent. In this chapter we show that they maintain the so-called fundamental relationships — and that, knowing one of them and the quadrant of $x$, it is always possible to calculate the other five.
