Question

use the sum and difference identities to find the cosine angle

cos pi/9 cos pi/3 - sin pi/9 sin pi/3

I do not know how to solve this because pi/9 is not on the unit circle.

Answer 1

but it gave you a hint, ...
cos(A+B) = cosAcosB - sinAsinB

does the right side not follow the pattern of your question?

so ...
cos pi/9 cos pi/3 - sin pi/9 sin pi/3
= cos(pi/9 + pi/3)
= cos(4pi/9)

You are right, 4pi/9 radians, or 80 degrees, is not one of the standard angles on the unit circle, nor is it obtainable using combinations of our standard angles.