To the nearest degree, all of the following angles are solutions of the equation 2sin x + 4 cos 2x =3 except:

(1) 40 degrees
(2) 150 degrees
(3) 166 degrees
(4) 194 degrees

I don't know if you are supposed to do this by simply substiting, or actually solve the equation.

I will solve it

2sinx + 4cos 2x = 3
2sinx + 4(1 - 2sin^2 x) -3=0
2sinx + 4 -8sin^2 x - 3 = 0
8sin^2 x - 2sinx -1 = 0
sinx = (2 ± √36)/16 = 1/2 or -1/4


x = 30° or 150° or x = 194.4775..° or 345.522°

so to the nearest degree I got
x = 30, 150, 194 and 346

I see only two of these in your list, so the others don't work

To find out which of the given angles is not a solution of the equation 2sin x + 4cos 2x = 3, we can substitute each angle into the equation and check if the equation holds true.

Let's go through each option one by one:

(1) 40 degrees:
Substituting 40 degrees into the equation:
2sin(40) + 4cos(2 * 40) = 3
0.985 + 1.549 = 2.534

Since 2.534 is not equal to 3, 40 degrees is not a solution.

(2) 150 degrees:
Substituting 150 degrees into the equation:
2sin(150) + 4cos(2 * 150) = 3
-1 + 2 = 1

Since 1 is not equal to 3, 150 degrees is not a solution.

(3) 166 degrees:
Substituting 166 degrees into the equation:
2sin(166) + 4cos(2 * 166) = 3
-1.527 + 2.496 = 0.969

Since 0.969 is not equal to 3, 166 degrees is not a solution.

(4) 194 degrees:
Substituting 194 degrees into the equation:
2sin(194) + 4cos(2 * 194) = 3
0.177 + 2.313 = 2.49

Since 2.49 is not equal to 3, 194 degrees is not a solution.

So, after checking each option, we can conclude that all of the given angles (1) 40 degrees, (2) 150 degrees, (3) 166 degrees, and (4) 194 degrees are not solutions to the equation 2sin x + 4cos 2x = 3.