
                         Review of Trig Definitions.
                         ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀

You MUST have the following information at your fingertips at all times.
If you don't, you have NO CHANCE of doing "well" in Calculus I, II, & III.
Unlike many other subjects, success in Mathematics depends critically on
the prerequisite material.

┌───────────────────┐
│ Basic Definitions │
└───────────────────┘

                                      B
                                     /▌
                                    / ▌
                                   /  ▌ 
                                c /   ▌ a  
                     Hypotenuse  /    ▌   Opposite side
                                /     ▌   
                               /______▌ 
                              A   b    C
                               Adjacent 
                                 side
                                                   2    2      2
       This is a right-angled triangle, so that   a  + b   =  c  .
 
       If        angle CAB  =  α    (alpha)
    
       then
    
              sin α = a/c  (Opposite/Hypotenuse)
              cos α = b/c  (Adjacent/Hypotenuse) 
              tan α = a/b  (Opposite/Adjacent) 
              cot α = b/a  (Adjacent/Opposite)   = 1 / tan α
              sec α = c/b  (Hypotenuse/Adjacent) = 1 / cos α
              csc α = c/a  (Hypotenuse/Opposite) = 1 / sin α

┌─────────────────────┐
│ Radians and Degrees │
└─────────────────────┘

Although many calculus problems are posed in terms of degrees, calculations
are almost always done in radians.  You must be able to switch from one set
of units to the other without sweating.  The conversion is simple, if you
remember

                       18O°  =  π radians

so, remember it!

┌──────────────┐
│ Basic Values │
└──────────────┘

   ┌──────────╥─────────┬─────────┬─────────┬─────────┬─────────┐
   │ Angle    ║    O    │   π/6   │   π/4   │    π/3  │   π/2   │
   ╞══════════╬═════════╪═════════╪═════════╪═════════╪═════════╡
   │ SINE     ║    O    │   1/2   │  √2/2   │   √3/2  │    1    │
   │ COSINE   ║    1    │  √3/2   │  √2/2   │    1/2  │    O    │
   └──────────╨─────────┴─────────┴─────────┴─────────┴─────────┘

These particular values are used frequently in calculus problems, and every 
instructor assumes you can recite them at any time.  If you can't - GOODBYE!


┌───────────────────────┐
│ Elementary Identities │
└───────────────────────┘

                        sin (-x)  =  - sin x

                        cos (-x)  =  cos x

                           2       2
                        sin x + cos x  =  1

                           2             2
                        tan x + 1  =  sec x

                               2         2
                        1 + cot x  =  csc x


These last two identities can be obtained from the previous one very easily.
As an exercise you should make sure you can obtain them that way.

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