How to make the mesh color on 2D plot automatically same with the plot color? The code below doesn't work and produces "Automatic is not a graphics directive" error message.

    Plot[Sin[x], {x, 0, 2 Pi}, Mesh -> 10, MeshStyle -> Directive[PointSize[Large], Automatic]]

[![enter image description here][1]][1]

I am expecting an output which looks like this.

[![enter image description here][2]][2]

Second question, how to set different mesh size on more than one plot using single plot command? Tor example, I want to set mesh size 10 on `Sin` and mesh size 20 on `Cos`. Of course the mesh color must be automatically aligned with the color of respective plot. Same as the previous code, this one doesn't work and also produces "Automatic is not a graphics directive" error message.

    Plot[{Sin[t], Cos[t]}, {t, 0, 2 Pi}, Mesh -> {10, 20}, 
     MeshStyle -> Directive[PointSize[Large], Automatic]]

[![enter image description here][3]][3]

I am expecting this output.

[![enter image description here][4]][4]

I use *Mathematica* 10.2 on Windows 10 64bit. Thank you.

**Comment:** Thanks for all the answers. I didn't know this simple task needed relatively complex codes to solve. I was expecting something as simple as

    Plot[{Sin[t], Cos[t]}, {t, 0, 2 Pi}, PlotStyle -> {Red, Blue}]

Maybe WRI can make simpler solution in the future.


  [1]: https://i.sstatic.net/XBX8B.png
  [2]: https://i.sstatic.net/o01SY.png
  [3]: https://i.sstatic.net/vG7VR.png
  [4]: https://i.sstatic.net/ZRiqD.png