Some Basic Trig
by Chiem Whua Ma 


First, draw the chart below with 
SIN TAN SEC on left, CO-functions 
on right, and 1 in the middle.

        +---------------+
        |               |
        |  SIN-----COS  |
        |    \     /    |
        |     \   /     |
        |      \ /      |
        |  TAN--1--COT  |
        |   |  / \  |   |
        |   | /   \ |   |
        |   |/     \|   |
        |  SEC     CSC  |
        |               |
        +---------------+

Using this chart (I just look at it in my head) you can remember the following things:

Across the 1:
1/SIN = CSC or 1/CSC = SIN
1/TAN = COT or 1/COT = TAN
1/SEC = COS or 1/COS = SEC

Down any triangle:
SIN2 + COS2 = 1
TAN2 + 1 = SEC2
1 + COT2 = CSC2

Up any triangle:
SEC2-1 = TAN2
or 1-TAN2 = SEC2

CSC2-1 = COT2
or CSC2-COT2 = 1

1-SIN2 = COS2
or 1-COS2 = SIN2

A function and its two nearest CLOCKWISE or COUNTERCLOCKWISE neighbors around any edge of the square:

(listed starting at TAN going clockwise)
TAN = SIN/COS
SIN = COS/COT
COS = COT/CSC
CSC = SEC/TAN
SEC = TAN/SIN

(listed starting at TAN going counter-clockwise)
TAN = SEC/CSC
SEC = CSC/COT
CSC = COT/COS
COS = SIN/TAN
SIN = TAN/SEC

A function and its two neighbors around any edge of the square:
(listed starting at TAN going clockwise)

TAN = SIN*SEC
SIN = COS*TAN
COS = COT*SIN
CSC = COT*SEC
SEC = TAN*CSC


Don't forget to put in the arguments in each of the identities above!!


Send any comments or questions to: David Pleacher