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Consider the graphs of and .  

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

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

  2. Sketch the graph of . What is it equivalent to?

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

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

    Circle, with vertical & horizontal diameters, Increasing dashed line through the center, intersecting the circle at a point, labeled, open parenthesis, +, comma + close parenthesis,  about 1 fourth of the way in top right quadrant, and at a point, labeled, open parenthesis, negative, comma negative, close parenthesis, in third quadrant, with central angle in first quadrant, labeled, alpha.