When Dede woke up in the morning the temperature was 62 degrees outside. When Dede went outside for recess at school the temperature had gone up to 89 degrees.

0,pi, 7pi/6, 11pi/6

Step-by-step explanation:

Let x = theta

sin x +1 = cos 2x

Subtract cos 2x from each side

sin x +1 - cos 2x = cos 2x- cos 2x

sin x +1 - cos 2x = 0

We know that 1 - cos 2x = 2 sin ^2 x

sin x + 2 sin^2 x = 0

Let y = sin x

y + 2 y^2 =0

Factor out a y

y( 1+2y) =0

Using the zero product property

y=0  1+2y =0

y=0   2y =-1

           y = -1/2

Substituting back in for y

sin x =0          sinx = -1/2

Taking the inverse sin on each side

arcsin sin x = arcsin 0         arcsin sin x = arcsin (-1/2)

x = 0 + 2 pi n                                         x = 7 pi/6 + 2*pi*n

  = pi +2 pi n                                             = 11 pi/6 + 2 pi n

                         where n is an integer

We want solutions between and including 0 to 2pi

0,pi, 7pi/6, 11pi/6