y(x)=sin^2 (x/4)+12sin(x/4)
y(x) = sin^2(x/7) +16sin(x/7)
From the Chain Rule,
y'(x) = 2sin(x/4)*(1/4)cos(x/4) + 12(1/4)cos(x/4).
At x=4pi, the slope of the tangent line is
y'(4pi) = 2sin(4pi/4)*(1/4)cos(4pi/4) + 12(1/4)cos(4pi/4).
= 2sin(pi)*(1/4)cos(pi) + 12(1/4)cos(pi)
= 2(0)(1/4)(-1) + 12(1/4)(-1)
= -3
The angle (in radians) that the tangent line makes to the
positive x-axis is
pi - arctan(3)= 1.249 rad =71.565 degree
