Final answer:
To solve the equation cos x + 3sin x = 3 for 0 < x < 360, we can rewrite it and solve for sin(x). Then, we use the inverse sine function to find the values of x in the given range.
Step-by-step explanation:
To solve the equation cos x + 3sin x = 3 for 0 < x < 360, we can rewrite it as 1-4sin^2(x/2) + 3sin(x) = 3.
Let's substitute sin(x) = 2t. Now the equation becomes -4t^2 + 6t - 2 = 0.
Solving this quadratic equation, we get t = 1/2 or t = 1.
Substituting back sin(x) = 2t, we have sin(x) = 1/2 or sin(x) = 1. To find the values of x in the given range, we use the inverse sine function:
x = 30°, 150°, 90°, 270°.