Question

Write the equation of the tangent drawn to the curve y= sin x at the point (0,0)

Answer 1

First find the slope m  of the tangent evaluating the derivative at the point of interest:

y' = e^x (sin) x + e^x cos(x) this is called the product rule.

evaluate this derivative at x = 0:

y' = (0) = 0 + 1 = 1 = m

Use the relationship

y - y base 0 = m (x -x base 0)

to find the equation of the tangent:

y - 0  = 1 (x-0)

y = x