Find the linearization L (x) of the function at a.

f (x) = sin x, a=pi/6

As is it tangent line

by using slope formula

y-y1 = m (x-x1)

given a=pi/6=x1

f (x) = sinx

above equation can be wriiten as

f (x) - f (a) = f’ (a) (x - a)

so L (x) = f’ (a) (x-a) + f (a)

f (x) = sinx = f (pi/6) = 1/2 = y1

f’ (x) = cosx f’ (pi/6) = 3/2 = m

now putting values

L (x) = √ 3/2 (x-pi/6) + 1/2

L (x) = (√ 3/2) x+6-pi√ 3/12