Consider the tangent line to the curve $y = 10\sin(x)$ at the point $(\frac{\pi}{6}, 5)$.
(a) Find the unit vector that lies in the first quadrant that is parallel to the tangent line.
\boxed{} i + \boxed{} j
(b) Find the unit vector that lies in the fourth quadrant that is perpendicular to the tangent line.
\boxed{} i + \boxed{} j
(c) Sketch the curve $y = 10\sin(x)$ and the vectors in parts (a) and (b), all starting at $(\frac{\pi}{6}, 5)$. (Do this on paper. Your instructor
may ask you to turn in this work.)