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12-15.

If , what must be true about the sign of:

Graph each function using the input bar below or on your graphing calculator. What do you observe about the -values when is between and /2?

When graphing using the input bar, sin() is equivalent to sin().    

  1. sin(θ)

    The -values are negative.

    Line graph, with 5 horizontal lines, creating 4 spaces. Points are connected from left to right in these spaces as follows: 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3. Note: within each space, there is variability in the points' heights.

  2. cos(θ)

    Use the same method as part (a). It might also help to think about how the sin() and cos() graphs relate to each other.

  3. tan(θ)

    Use the same method as part (a).

    positive

  4. Does taking the reciprocal of something change its sign?