Here's a problem that I have to do for my pre-cal class:
An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 ≤ x ≤ pi, where x is expressed in radians.
Solve algebraically for all values of x in the interval 0 ≤ x ≤ pi, where the height of the opening, f(x), is 6. Express your answer in terms of pi.
If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel?
I thought I should set f(x) to 6 and solve the equation, which I did, and I got 30 as my answer. But that doesn't make sense because the answer is supposed to expressed in terms of pi, and is supposed to be less than pi. I don't know how else to solve this problem, if anyone could help that would be great! Thanks