Chapter 12.2, Problem 42E

To determine

Part (a):

To find:

The unit vectors that are parallel to the tangent line to the curve $y=2\sin x$ at the point $\left(\frac{\pi }{6},1\right)$

To determine

Part (b):

To find:

The unit vectors that are perpendicular to the tangent line to the curve $y=2\sin x$ at the point $\left(\frac{\pi }{6},1\right)$

To determine

Part (c):

To sketch:

The curve $y=2\sin x$ and the vectors in part (a) and (b), all starting at $(\pi /6, 1)$