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


5

6
4


2
3

6
6
2

6

6
0
First things first. You must know radians as well as you know degrees. Radians are your favorites.

3

2
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 2 π.
7

3
 
3
19

6 6

6

Having trouble figuring out what quadrant everything
4

6
 goes in? Here is one method:


30

5
6
QII
3


45
60



Eh, it’s not the greatest, but it’s an option.
0

6
You could try working common denominators.
5

3

6
6

9

6 6 6
I II III IV
12

6
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!!!!

30


6
1
2
3

2

3

45

4
1

2
2
2
2
2
1
2

60

1

2

1
2
Big  Small: Divide
Small  Big: Multiply
3 2
3
Remember, radius of unit circle is 1.
Radians
Degrees

Cos, sin goes with what?
Darn, what’s the first coordinate?

.
8
Positive or Negative?
Radians, Degrees Conversion?

.
5

6



2
3
,
1
2


You can go with ASTC
S A
T C
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.
Just remember that π = 180 o , and put everything in the right place, π with radians, 180 o with degrees. rad

 deg
180


A) Factor out the coefficient of x, and use even-odd properties to simplify
1) Find Amplitude and period
2) Find Phase Shift, and vertical shift
3) Find starting and ending x-coordinates
4) Divide into 4 equal parts
5) Label key points
6) Connect
Amplitude =
T =
P.S. =
2



2
+

3
1 y
 
3 cos(
  x
3

5

2

3

)
5
4

5

2

2 y y



3 cos(
 

3 cos(

(
( x x


3 ))

3 )) 2
2
3
Remember, cos(x) = cos(-x)
3

2
4

You will always do this, this is part of
2 your ‘work’ on a test and is required
You want to study the sine and
Starting point is phase shift. Ending cosine graphs. Remember: point is Phase shift + Period
Sine  0, 1, 0, -1, 0
You will take the starting and ending
V.S. =

1) Start with a quick sketch of the first quadrant, unit circle values, and radian denominators.
2) Identify denominator of the problem.
3) Locate quadrant.
4) Follow rectangle, attach correct sign, use x for cosine, y for sine sin
2
3


2
3 cos
7

4

2
2
Try these problems
(next click will bring up all solutions) cos
6
5
 sin
7

3
 
2
3
 
2
3
11
 cos sin
5

6
6


1
2
2
3
( 0 , 1 )
S A
T C


1
2
,
2
3





3
2
2
,


2
2
2
3



,
1
2


4
6
( 1 , 0 )
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.

A) Make sure all values are reduced
1) Start with unit circle values next to denominators. Also, ASTC diagram.
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.
S A
T C
Key is to be quick with your quadrants, and keep things neat and watch out for signs.
 cos

3 sin
4 cos

11

6
4
 sin
3








1
2
,
2
2
,
2
1
2
,
3
,
1
2


2
3


2
3


2
2


Positive
Positive
Positive
Negative


1
2
,
2
3




2
2
,
2
2




2
3
,
1
2


3
4
6

 cos
6
4
 sin

3 cos
2
11
 sin
6
5
 cos
4
2
 sin
3
2
 cos

3 sin
4 cos
 sin
7
6
3


4

 
2
3
2
3

0


1
2
 
2
2

3
2
 
1
2

2
2
 

2
2
2
3
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 =^- )

 cos
2

6 sin
3
7
 cos
2
7
 cos cos sin cos
3
11
 sin
9

6
4
13
 cos

4
5

6 sin
3
5

4

2
3


0
2
3



2
2
2
3
2
2

1
2
 



1

1
2
2
2
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 =^- )