The angle at which the curve $y=k{e}^{kx}$ intersects the y-axis is

curve  intersects  y-axis,  x=0
                                                   y=k
point on the curve is (0,k)
$\frac{dy}{dx}=k^2{e}^{kx}$ 
${\left(\frac{dy}{dx}\right)}_{(0,k)}=k^2$ 
$\therefore \tan \theta =k^2$       ($\theta$  is angle with  x-axis  )  
Angle with y-axis  ;  $\frac{\pi }{2}-\theta$ 
$=\frac{\pi }{2}-{\tan }^{-1}\left(k^2\right)$ 
${\cot }^{-1}\left(k^2\right)$
                                                       
$\sec =\sqrt{1+{\tan }^2\theta }$
$\sqrt{1+k^4}$
$\sin \theta =\frac{1}{\sqrt{1+k^4}}$               

$\theta ={\sin }^{-1}\left(\frac{1}{\sqrt{1+k^4}}\right)$