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## Homework Statement

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?

## Homework Equations

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

Please help!!

However the book says the answer is θ = φ/2 + pi/4

Did I make an error?