Question

Problema 10. Encuentre el valor de x que satisface la siguiente ecuación trigonométrica para ángulos entre 0°≤ x ≤ 360°.

2sen^2 (⁡x)+cos⁡(x)-1=0

Answer 1

${2\sin^2(x) + \cos (x) - 1 = 0}\\ \\{ 2(1-\cos^2(x)) + \cos (x) -1 =0}\\ \\ {2-2\cos ^2(x)+\cos (x) -1=0}\\\\{2\cos^2(x)-\cos (x)-1=0}\\\\{(2\cos (x)+1)(\cos (x) -1)=0}\\\\\\\\{\cos(x)= -1/2}\\\\{x= 120^{\circ} , 240^{\circ}}\\\\\\{\cos (x)=1}\\\\{x= 0^{\circ}, 360^{\circ}}\\\\\\{\text{salu2. :)}}$