Question

Find the equation of the tangent line to the curve y = 2sinx at the point (pi/6,1). The equation of this tangent line can be written in the form y = mx+b. Compute m and b

Answer 1

y = 2sinx
dy/dx = 2cosx
When x = π/6, dy/dx = 2cos(π/6) = sqrt(3)
y - 1 = (sqrt(3))(x - π/6)
y = (sqrt(3))x + (1 - πsqrt(3)/6)
So m = sqrt (3), b = 1 - πsqrt(3)/6