Question

Find an equation of the tangent line to y = 2 sin x at x = π/6

Answer 1

Equation of the tangent line:
y-y0 = f´(x0)(x-x0)
x0 = π/6, y0= 2 sin(π/6)= 1
f´(X)=2 cos x
y - 1 = 2 cos(π/6)(x- π/6)
y - 1 =
`2 * ( √(3) )/(2) ( x - ( \pi )/(6) )`
y =
`√(3) (x - ( \pi )/(6) )+ 1 \\ y= √(3) x + (1- √(3) \pi )/(6)`