What angle does the tangent to the curve y(x)=sin^2(x/3)+15sin(x/3) at x=3pi make with the x-axis?

Answer 1

dy/dx = 2(1/3)sin(x/3) cos(x/3) + (1/3)(15)cos(x/3)

at x = 3π
dy/dx = (2/3)sinπ cosπ + 5cosπ
= 0 + 5(-1) = -5

angle that tangent makes is tan^-1 (-5) = 101.3°

Answer 2

I'd rather pick -78.7°

As x is increasing, y is decreasing.
Also, the principal values of tan^-1 are -π/2 to π/2