The document summarizes trigonometric functions and their relationships. It discusses the unit circle, radians vs degrees, computing trig ratios using the unit circle, trig identities, trig functions and their properties including amplitude, frequency, phase and period. It provides examples of trig functions and applications to modeling periodic behavior like sound waves and tides. Practice problems at the end involve converting between radians and degrees and expressing trig ratios as radicals.

2. Review Starting with a right triangle, like the one pictured on the right, three basic trig ratios are defined as follows:

3. Review Three additional trig ratios are defined from the basic ratios as follows: Table of Contents

5. The Unit Circle Radians vs. Degrees The conversion from radians to degrees or the other way around uses the equation: Convert 120 ° to radians by solving the equation: Cross multiply to solve for x :

6. The Unit Circle Radians vs. Degrees The conversion from radians to degrees or the other way around uses the equation: Cross multiply to solve for x : Convert radians to degrees by solving the equation:

9. The Unit Circle Computing Trig Ratios These trig ratios are summarized in the following table: Table of Contents

11. Trig identities cos (  -  ) = -cos (  ) sin (  -  ) = sin (  ) tan (  -  ) = -tan (  ) From the first to the second quadrants x changes sign while y remains positive. As  is swept up away from the positive and negative x -axis, equal angle sweeps are related as:  :  -  . These characteristics lead to the following relationships:

12. Trig identities - Examples : a.) second quadrant: b.) fourth quadrant: c.) third quadrant:

27. Practice: Express the following trig ratios as multiples of a simple radical expression:

28. Practice: Express the following trig ratios as multiples of a simple radical expression:

29. Match the curve to the equation: Practice: A. B. C. B A C