14.4: Summary

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This chapter introduced and reviewed angles, cyclic processes, trigonometric, and periodic functions
amplitude, period, frequency, and phase were defined and identified with graphical properties
the functions cosine and sine correspond to $(x, y)$ coordinates of a point moving around a circle of radius $1 . \tan (x)=\sin (x) / \cos (x)$ is their ratio.
rhythmic processes can be approximated by a sine or a cosine graph once the period, amplitude, mean, and phase shift are identified.
to define an inverse trigonometric function, the domain of the original trig function has to be restricted to make it one-to-one (no repeated $y$ values).
Applications addressed in this chapter included:
1. electrocardiograms detecting the electrical activity of the heart;
2. daylight hours fluctuating with period of one year;
3. hormone levels that change on a daily rhythm; and
4. phases of the moon, with a $29.5$ day period.

What is the range of the function $y=8 \sin (2 t)$ ?
Does a phase shift change the period of a trigonometric function?
If, in a 1-minute interval, a heart beats 50 times, what is the length of a heart beat cycle?
Using the following right angle triangle, determine:

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