Test III Review Sheet for
Colorado State University, Pueblo
Math 124 — Pre-calculus Math — Spring 2015

Topics

Things we discussed, which you should be able to work with:
  1. terminal point corresponding to a real number
  2. definition of sin, cos, tan, csc, sec, and cot in terms of terminal points
  3. trig functions of certain special values such as $\pi/6$, $\pi/4$, $\pi/3$, $\pi/2$.
  4. signs of the trig functions for values with corresponding terminal points in various quadrants
  5. even/odd properties of trig functions
  6. the three Pythagorean identities
  7. periodicity properties of the trig functions
  8. amplitude, period, and phase shift for trig functions
  9. graphing trig functions and recognizing their graphs
  10. restricted domains to make the trig functions 1-1
  11. definitions of the inverse trig functions, their domains and ranges
  12. amplitude, period, and frequency of a function used to model a simple harmonic oscillator
  13. a formula which models a damped harmonic oscillator
  14. degrees, radians, and converting between them
  15. arc length and area of a circular sector
  16. angular speed v.s. linear speed
  17. trig functions for acute angles: SOHCAHTOA (only in right triangles)
  18. trig functions for arbitrary angles, using the reference angle and adusting the sign
  19. reciprocal and Pythagorean identities (again)
  20. solving a triangle
  21. the area of a triangle from side lengths and the angle between them
  22. the Law of Sines
  23. the Law of Cosines
  24. solving many more triangles
  25. Heron's formula

Format of the test

There will be problems from the material corresponding to each section we've done in the textbook, of a level of difficulty and wording similar to the problems which you have done for homework and quizzes. The total points for the test will be well more than 100, you can choose which 100 points you want to do out of the available problems.

To get credit for a solution on the test, you must always explain your work;correct answers without explanation usually are worth zero points. Also, whenever possible, give exact answers — e.g, if the answer to a problem is $\sqrt{2}$, please write that, do not write $1.41421356237309504880168$, no matter how tempting.

Don't forget your calculator, you will need it!