Question

Find an equation of the tangent line to the curve y=arccos(x/2) at the point (1,4pi)

Answer 1

The derivative of inverse trigonometric identities follow a set of rules. 
For arc cos x, the dy/dx is equal to -1/ square root of (1 - x2). 
In this case, we still have 1/2 x inside the angle quantity so we multiply the dy/dx above with 1/2. Hence, y' = is -1/ 2 square root of (1 - x2); x = 1, y' is infinity. this means the line is horizontal. The answer hence is y = 1.