Consider the graphs of $y = \sin\left(x + π\right)$ and $y = -\sin\left(x\right)$.  

1. Sketch both graphs on separate axes. What do you notice?

   Hint (a):

   The first curve is shifted left $π$ units.
   The second curve is reflected vertically.

2. Sketch the graph of $y = \cos\left(x + π\right)$. What is it equivalent to?

   Hint (b):

   Look at the equations of the curves and the hint in part (a).

3. Use the unit circle to explain why adding $π$ to the angle $x$ reverses the sign of the $x$- and $y$-coordinates.

   Hint (c):