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4-57.
  1. Consider the graphs of y = sin(x + ) and y = −sin x. Homework Help ✎

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

    2. Sketch the graph of y = cos(x + ). What is it equivalent to?

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

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

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