Question

sabendo que π/6 é a raiz da equação cos²x - m . senx + 1 = 0 determine m

Answer 1

π/6 = 30

cos² . x - m . senx + 1 = 0
cos² . 30 - m . sen30 + 1 = 0
cos 30² - m . 1/2 + 1 = 0
(V3/2)² - m/2 = -1
3/4 - m/2 = -1
-m/2 = -1 - 3/4
-m/2 = (-4-3)/4 .(-1)
m/2 = 7/4
m = 7.2/4
m = 14/4
m = 7/2

Answer 2

 Olá Renan,


$\cos^2x-m\cdot\sin\,x+1=0\\\\\left(\cos\frac{\pi}{6}\right)^2-m\cdot\sin\frac{\pi}{6}+1=0\\\\\left(\frac{\sqrt{3}}{2}\right)^2-m\cdot\frac{1}{2}+1=0\\\\\frac{3}{4/1}-\frac{m}{2/2}+\frac{1}{1/4}=0\\\\3-2m+4=0\\\\2m=7\\\\\boxed{m=\frac{7}{2}}$