APL (dzaima/APL), 57 bytes

^{No MATL answer here yet! yay!}

{n←⍺⋄P5.G.circle 3⍴30⋄{P5.G.ln↑30×1+2 1○ᑈ1n×⍵×○2÷k}¨⍳k←⍵}

Draws a 30x30 circle with the times table for n and k.

Function submission which takes arguments as n f k, and will display properly on a default sized canvas.

This uses the formula from user58543's answer.

You can test this out using this file and dzaima's APLP5 engine.

Explanation:

{n←⍺⋄P5.G.circle 3⍴30⋄{P5.G.ln↑30×1+2 1○ᑈ1n×⍵×○2÷k}¨⍳k←⍵}
{n←⍺⋄                                                   k←⍵} store left arg in n and right arg in k
      P5.G.circle 3⍴30⋄                                      Draw circle of radius 30

                                                        ⍳k   generate range 1..k
                       {                              }¨     Execute the following for each number i:
                                            1n×⍵×○2÷k        Multiply [1,n] with i×2π/k
                                      2 1○ᑈ                  Take cos and sin of each of those
                                30×1+                        Multiply 30, add 30 to them
                              ↑                              Convert to matrix
                        P5.G.ln                              Plot a line using those coordinates

Output for n=5, k=10: