f(x)=2sinx=8cos(1/2)x???
pi/6 is 30 degrees.
So it's 2 times sin (30 degrees) minus 8 times cos (15 degrees).
But I'm assuming a level of mathematics which is higher than just looking stuff up in tables yeah? In which case you might want to try the half-angle formulae to express that cos in terms of things which have pi/6's in so you can use the standard values of sin and cos of pi/6. Have fun.