Some members here may have seen this problem before. The problem is:
A projectile is fired up an incline (incline angle φ) with an initial speed, v ,at an angle θ with respect to the horizontal (θ>φ). What is the angle that will allow the projectile to travel the maximum distance, r , along the incline plane and what is that value of r?
r(θ) = [2(v^2)cos(θ)sin(θ-φ)]/g(cos^2(φ))
The Attempt at a Solution
When I differentiate r(θ) and set it equal to zero, I get the equation cot(2θ) = -tan(φ) which then becomes cot(2θ) = -cot(pi/2 - φ) because of the identity
cot(pi/2 - x) = tan(x).
Thus, 2θ = -(pi/2 - φ) and θ = φ/2 - pi/4
However the book says the answer is θ = φ/2 + pi/4
Did I make an error?