MHB Need help understanding phase shift in trigonometric curves

[charki126]

At what value of α is the curve y=asin2π/λ (x+α) in phase with z=asin2π/λ(x)?

My answer booklet says α=1−λx+nλ, but I keep getting α=nλ, where n=0,1,2...
I have no clue how to get to the answer shown in the mark scheme. Any insight would be much appreciated!

 

[skeeter]

Guessing at your syntax ... are the following interpretations correct?

$y = A\sin\left[\dfrac{2\pi}{\lambda} \cdot (x + \alpha)\right]$

$z = A\sin\left(\dfrac{2\pi}{\lambda} \cdot x \right)$

If so, then the period of both sinusoids is $\lambda$, hence I agree that the two will be in phase for $\alpha = k \lambda \, , \, k \in \mathbb{Z}$