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Figure 2.6.2 is repeated below, on the left side of Figure 2.7.1. It shows $\tan(\theta)$ in relation to $\theta$.
The animation on the right of Figure 2.7.1 shows the value of $\tan(x)$ in relation to the value of x in the x-y plane, where x is in radians.
Study the animations in Figure 2.7.1 until you see the same thing happening in both animations.
Reflection 2.7.1. The vertical axis in Figure 2.7.1 (right) is labeled "y (radians)". Is that appropriate, or should it be labeled "y (radii)"?
Reflection 2.7.2. What do you think the faint vertical lines mean in the graph of $y = \tan(x)$?
Reflection 2.7.3. Does tan(x) ever decrease? What does it mean for a function to decrease?
Reflection 2.7.4. At what values of x does the graph of $y = \tan(x)$ "break"? Remember, values of x are in radians.
Use the graph of $y = \cos(x)$ and the definition of the sec function to explain why the graph of $y = \sec(x)$ behaves as it does.
Use the graph of $y = \sin(x)$ and the definition of the csc function to explain why the graph of $y = \csc(x)$ behaves as it does.
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