For which value of the parameter A does the sinusoid y=A

For which value of the parameter $A$ does the sinusoid $y=A\sin\dfrac{x}{a}$ intersect the $Oy$ axis at an angle of $45°$?

Step 1: Slope at the origin

The curve passes through $(0,0)$, and $y'=\dfrac Aa\cos\dfrac xa$, so $k=y'(0)=\dfrac Aa$.

Step 2: The angle condition

The angle between the tangent and the vertical $Oy$ axis is $90°-\arctan|k|$; setting this to $45°$ forces $\arctan|k|=45°$, i.e.\ $|k|=1$: \[\left|\frac Aa\right| = 1 \;\Longrightarrow\; A = \pm a. \tag{1}\]