Verified answer

The quadratic formula is the ugly way to solve this one. Substitution is simpler and more elegant. Let u = sin x:

18sin²x - 13sinx + 2 = 0

18u² - 13u + 2 = 0

(2u-1)(9u-2) = 0

u = ½ and 2/9

sin x = ½ and 2/9

sin x = ½

x = arcsin(½)

x = π/6 ≅ 0.524

sin x = 2/9

x = arcsin(2/9)

x ≅ 0.224

The answer is C.

18*sin²(x) - 13*sin(x) + 2 = 0

18*sin²(x) - 9*sin(x) - 4*sin(x) + 2 = 0

9*sin(x)(2*sin(x) - 1) - 2(2*sin(x) - 1) = 0

sin(x) = 2/9 and sin(x) = 1/2

x = pi/6 and x = arcsin(2/9)*pi/180

Answer: C