Question

What angles could we find sine and cosine for using information for π/4 and π/6?

Answer 1

Had to do a bit of guesswork to figure out what you're asking here.  If you're given the 2 angles pi/4 and pi/6, you can find any trig function of either angle.

The sine of pi/4 is  1 / sqrt(2); the cosine is the same.

The cosine of pi/6 is sqrt(3) / 2; the sine of pi/6 is 1/2.

If this isn't quite what you were looking for, try paraphrasing your question to make it clearer.