Question

Anonim Help me. 3-4cos^2 t=0 2 cos^2 t-cos t = 0 4 cos^2 t-1=0 2 cos^2 t+cos t = 0

Answer 1

$1)3-4cos^2 t=0 \\4cos^2t=3 \\cos^2t= \frac{3}{4} \\cost= \sqrt{\frac{3}{4} }= \frac{\sqrt{3}}{2} \\t_{1,2}=\pm \frac{\pi}{6} +2\pi n,\ n \in Z \\cost=- \sqrt{\frac{3}{4} }= -\frac{\sqrt{3}}{2} \\t_{3,4}=\pm \frac{5\pi}{6} +2\pi n,\ n \in Z \\2)2 cos^2 t-cos t = 0 \\cost(2cost-1)=0 \\cost=0 \\t_1= \frac{\pi}{2} +\pi n,\ n \in Z \\2cost=1 \\cost= \frac{1}{2} \\t_{2,3}= \pm \frac{\pi}{3} +2\pi n,\ n \in Z$
$3)4 cos^2 t-1=0 \\4cos^2t=1 \\cos^2t= \frac{1}{4} \\cost=\sqrt{\frac{1}{4} }= \frac{1}{2} \\t_{1,2}= \pm \frac{\pi}{3} +2\pi n,\ n \in Z \\cost=-\sqrt{\frac{1}{4} }= -\frac{1}{2} \\t_{3,4}=\pm \frac{2\pi}{3} +2\pi n,\ n \in Z \\4)2 cos^2 t+cos t = 0 \\cost(2cost+1)=0 \\cost=0 \\t_1= \frac{\pi}{2} +\pi n,\ n \in Z \\2cost=-1 \\cost= -\frac{1}{2} \\t_{2,3}=\pm \frac{2\pi}{3} +2\pi n,\ n \in Z$