Question

Qual o conjunto solução para a seguinte equação trigonométrica, considerando o intervalo entre 0º e 360º? cos²x + sen x – 1 = 0

Answer 1

$\displaystyle \sf cos^2x+sen\ x-1=0 \\\\\ 1-sen^2x+sen\ x-1=0\\\\ sen^2x-sen\ x=0 \\\\ sen\ x\cdot (sen\ x-1)=0 \\\\ sen\ x = 0 \to \ x = 0 \ \ ou \ \ x = \pi \ \ ou\ \ x = 2\pi \\\\ sen \ x -1=0 \to sen\ x=1 \to x= \frac{\pi}{2} \\\\\\ \underline{Conjunto\ Solu{\c c}{\~a}o}: \\\\ \huge\boxed{\sf S = \left\{0,\ \frac{\pi}{2},\ \pi,\ 2\pi \right\} }\checkmark$