Question

A. pi/3b. pi/3, 5pi/3c. 0, pi/3, 5pi/3d. pi/3, 5pi/3, pi

Answer 1

d. pi/3 , 5 pi/3 , pi

Use the identity:

sin^2 x + cos^2 x = 1

Solve the quadratic by factoring and completing the square:

2sin^2 x + cos x = 2 (1 - cos^2 x ) - cos x

= -2 cos ^ x - cos x +2

= 1

2 cos^2 x+ cos x -1 = 0

(2 cosx-1 ) (cosx + 1 ) =0

SO:

cos x = 1/2 or cos x =-1

Cos x is positive for 0

x= pi/3 , or pi ,or 5/3 pi