Question

Se sen a=p e cos a =q, determine em função de p e q as expressão:
(EXPRESSÂO ESTA NA IMAGEM)

Answer 1

$\displaystyle \sf Arcos \ soma/subtra{\c c}{\~a}o : \\\\ sen(x+y) = sen\ x\cdot cos\ y +sen\ y\cdot cos\ x \\\\ sen(x-y) = sen\ x\cdot cos\ y -sen\ y\cdot cos\ x \\\\\\ cos(x+y)=cos\ x\cdot cos\ y -sen\ x \cdot sen\ y\\\\ cos(x-y)=cos\ x\cdot cos\ y +sen\ x \cdot sen\ y$

Temos :

$\displaystyle \sf sen\ a = p \ \ ,\ \ cos \ a = q \\\\\ \frac{cos\left(\frac{\pi}{2}+a\right)}{sen\left(\frac{\pi}{2}-a\right)} \\\\\\ \frac{cos(\frac{\pi}{2})\cdot cos\ a -sen(\frac{\pi}{2})\cdot sen\ a }{sen(\frac{\pi}{2})\cdot cos\ a -sen\ a \cdot cos(\frac{\pi}{2})} \\\\\\ \frac{0\cdot cos\ a -1\cdot sen\ a }{1\cdot cos\ a -sen\ a \cdot 0 } \\\\\\ \frac{-sen\ a}{cos\ a} \\\\\\\ \huge\boxed{\sf \frac{-p}{q} } \checkmark$