Question

Com U= [0,pi[,resolva:
sen x + cos x =0

Gabarito: S={3pi/4,7pi/4}

Answer 1

$\large\boxed{\begin{array}{l}\sf sen(x)+cos(x)=0\\\sf supondo~cos(x)\ne0,vamos~dividir~tudo~por~cos(x):\\\sf \dfrac{sen(x)}{cos(x)}+\dfrac{cos(x)}{cos(x)}=\dfrac{0}{cos(x)}\\\sf tg(x)+1=0\\\sf tg(x)=-1\\\sf a~tangente~\acute e~negativa~no~2^o~e~4^o~quadrante\\\sf o~arco~cuja~tangente~vale~1~\acute e~\dfrac{\pi}{4}.\\\end{array}}$

$\large\boxed{\begin{array}{l}\sf no~2^o~quadrante~o~arco~equivalente~a~\dfrac{\pi}{4}~\acute e\\\sf \pi-\dfrac{\pi}{4}=\dfrac{3\pi}{4}\\\sf no~4^o~quadrante~o~arco~equivalente~a~\dfrac{\pi}{4}~\acute e\\\sf 2\pi-\dfrac{\pi}{4}=\dfrac{7\pi}{4}\\\sf portanto\\\sf S=\bigg\{\dfrac{3\pi}{4},\dfrac{7\pi}{4}\bigg\}\end{array}}$