**Module 4 - Topic 1 - Trigonometric Relationships**

"Trigonometric Relationships begins with triangle trigonometry. Students use what they know about trigonometric ratios to derive the area formula for any triangle, the Law of Sines, and the Law of Cosines. ... Students then explore how periodic functions are built. The scenario is then adapted so that it more closely resembles a unit circle, which students later use to identify sine and cosine of specific reference angles. ....The unit circle is then unrolled along the x-axis to demonstrate the key characteristics of periodic functions. Students then explore the tables and graphs of periodic functions for characteristics such as the maximum, minimum, period, amplitude, and midline." "Students then explore the unit circle to relate central angles to arc lengths. They are introduced to theta (θ) and use the ratio of arc length and the measure of the radius to derive radian measure. Once they understand radian measure, students convert between angle measures in degrees and radians." -Carnegie Textbook |
"Heartbeats can be periodic functions, though technically they don’t continue forever."
- Carnegie Textbook |