I am a Supplemental Instruction Leader for Indiana University East, and I have been blessed to do it for their M126 Trigonometric Functions course. The book it uses is Rockswold Precalculus with Modeling and Visualization (6th Edition). I love the book. 🙂
This page does not tell you what you need to know to pass the course, but the fundamentals I think you should know. My take is that, especially with the “Show Me an Example” feature of Pearson’s MML, you can get the homework done without understanding why you use a specific approach to get an answer.
Then that weak foundation only becomes clear during quizzes, exams, and later sections.
So, here is, by section, what I think you should know in addition to what your teacher wants. Notice how often the word “why” is used. 🙂
Oh, and part of the reason I love the book is that at the end of each section it has a tremendous summary of important items from the preceding material. That’s what I used to study. So, always, be sure to know the “Putting It All Together” for each section. However, there are times where that isn’t 100% true, depending on the teacher. That’s a good reason, if you are in a class I am SI leading for, to come to SI sessions. 🙂
- What are the standard position, vertex, initial side, and terminal side?
- What are the directions of rotation for positive and negative angles?
- Why is it called coterminal?
- What are complementary and supplementary angles? (Be able to see them, even when they aren’t obvious. This will be invaluable in later sections.)
- Why do you convert degrees to radians by multiplying by pi/180º and radians to degrees by multiplying 180º/pi?
- Why is the formula for arc length s=rtheta? (Think of a circle. What is the formula for its circumference using the radius? How many radians is a full circle’s “angle”?)
- Why is the area of a sector calculated by A=1/2 r^2theta? (Again, think of a circle. What is the formula for its area? And so on. :-))
- Why is angular speed calculated by w=theta/t and linear speed by wr? (Hint: Speed is always a value divided by time, and wr implicitly does that…essentially leveraging how you calculate the length of an arc with a value that already has been divided by time.)
- Speed is always positive; it does not care about direction. Velocity does.
- Know what is in 6.1’s “Putting It All Together” on pages 524 & 525. Especially know the definitions of the six standard trigonometric functions on page 524 (the ratios based on opposite, adjacent, and hypotenuse).
- Why do the confunction formulas work? (See “Putting It All Together” on page 525.) E.g. Why does sin alpha = cos(90º – alpha)? (Hint: In a right triangle, the two non-right angles swap adjacent and opposite sides and are complimentary.)
- To calculate the absolute value of the trig functions, you only care about the absolute value of the angular distance to the X axis. (Bonus: Why is that? Hint: the sides of your right triangle are x and y.)
- You can figure out the sign (positive of negative) of the trigonometric function by knowing which quadrant the angle is in.
- Related to the first two bullets, why are reference angles your friend? 🙂
- Remember that all trig functions are positive in two quadrants and negative in quadrants. Unless you have additional info to limit it to a single quadrant, there may be multiple answers.
- Algebra still works like algebra, even with trig functions involved. 🙂
E.g. 2sin(theta) = sqrt(3) would be solved the same way you would 2x = sqrt(3). E.g. let x = sin(theta). The only difference is that you have the final step of “undoing” the trig function (e.g. sin^-1).
- Plain old sin and cos cannot be more than 1 or less than -1. (Bonus: Why is that?)