Thinking about angles and quadrants

1. Here are some various memorization techniques. These may or may not be the best for you, but you can look through it and see if it helps or not. Perhaps a combination of methods may help. Please e-mail mistakes or suggestions to sakim@fjuhsd.net Thinking about angles and quadrants Rectangles Special Triangles Write and scratch What goes with what, I forgot. Practice 1 Graphing Practice 2

2. First things first. You must know radians as well as you know degrees. Radians are your favorites. I II III IV A quick way to work out the co-terminal angles without fumbling around too much is to just double the denominator. That is a quick way to find the equivalent of 2π. 6 times 2 3 times 2 Having trouble figuring out what quadrant everything goes in? Here is one method: You could try working common denominators. But nothing beats familiarity, so study your unit circle. You should be able to spot quadrants with radians as quickly as you would with degrees!!!! Eh, it’s not the greatest, but it’s an option.

3. 1 1 Big  Small: Divide Small  Big: Multiply Remember, radius of unit circle is 1. Radians 1 Degrees

4. If you forget, just remember cos is before sin alphabetically. So cos relates to x in the unit circle, and sin with y on the unit circle. Or common sense it with cos  x, sin  y, and look to see if x and y are positive or negative. Unless this clicks, ASTC might be easier. You can go with ASTC S A T C Cos, sin goes with what? Darn, what’s the first coordinate? Positive or Negative? In the first triangle, it’s longer on the bottom than it is tall. Radians, Degrees Conversion? Just remember that π = 180o, and put everything in the right place, π with radians, 180o with degrees.

5. A) Factor out the coefficient of x, and use even-odd properties to simplify • Find Amplitude and period • Find Phase Shift, and vertical shift • Find starting and ending x-coordinates • Divide into 4 equal parts • Label key points • 6) Connect 1 5 3 Amplitude = T = P.S. = V.S. = Remember, cos(x) = cos(-x) You will always do this, this is part of your ‘work’ on a test and is required + You want to study the sine and cosine graphs. Remember: Sine  0, 1, 0, -1, 0 Cosine  1, 0, -1, 0, 1 You are basically performing transformations on those key points Starting point is phase shift. Ending point is Phase shift + Period You will take the starting and ending points and find the average, then find the average again to break it up into four equal regions

6. 1) Start with a quick sketch of the first quadrant, unit circle values, and radian denominators. 2) Identify denominator of the problem. S A T C 3) Locate quadrant. 4) Follow rectangle, attach correct sign, use x for cosine, y for sine Try these problems (next click will bring up all solutions) The rectangles will hopefully become unnecessary as you work through these problems more and more. There are many variations of this method that are just as useful.

7. A) Make sure all values are reduced 1) Start with unit circle values next to denominators. Also, ASTC diagram. S A T C 2) Write down all the coordinates based on the denominator. 3) Cross out values you don’t want. Keep x for cosine, y for sine. 4) Figure out the quadrant, attach sign. Key is to be quick with your quadrants, and keep things neat and watch out for signs. Positive Positive Positive Negative

8. STOP When you click, the problems will appear. After 150 seconds (2.5 minutes), the word stop will appear. The next click will bring up the answers (hopefully they are correct =^- )

9. STOP When you click, the problems will appear. After 210 seconds (3.5 minutes), the word stop will appear. The next click will bring up the answers (hopefully they are correct =^- )