Find B and C and two solutions for g(x) = 12

Question

Let f(x)=2sin(3x)+4 for x∈R.

 

Let g(x)=5f(2x).

 

The function g can be written in the form g(x)=10sin(bx)+c.

The equation g(x)=12 has two solutions where π≤x≤34π​. Find both solutions. Write your answers correct to three significant figures.

Answer 1

g(x) = 10 sin (6x) + 20

12 = 10 sin (6x) + 20

-8 = 10 sin (6x)

-0.8 = sin (6x)

-53.13010 ≈ 6x