Could you help me by telling me if this is done correctly?
Find a function whose tangent line at the point $(1, 0)$ is parallel to the tangent line at the point $(\pi/2, \pi/2)$ of the curve $y = \theta \sin \theta$.
I first took the slope of the curve, derived it and substituted $\pi/2$ into the derivative and it gave me that the slope is $1$. Then, I used Taylor's formula for a polynomial of degree one, substituted the data and it gave me $f(x) = x-1$, the formula is $f(x) = f(a) + f'(a) \cdot (x-1) a = 1$ (the $x$ coordinate $(1,0)$) and $f'(a) = 1$ (the slope of the curve).