Question

Find the equation of the tangent line to the curve y=2sinx
y
2
sin
x
at the point (π/6,1)
π
6
1
.

The equation of this tangent line can be written in the form y=mx+b
y
m
x
b
where

Answer 1

 Hello
f(x) = 2sin(x)
f(π/6) = 1 
f'(x) 2cos(x)
f'(π/6) = 2×co(π/6) = 2 × root(3)×0.5  =root(3)
The equation of this tangent line is : y= root(3)(x-π/6)+1
y = root(3)x+1 - π/6(root(x))  in the form y=mx+b
m = root(3)   and   b = 1 - π/6(root(x))