How to construct Trigonometry table in 5 minutes without memorising ?

      Most of the students or learner who are studying trigonometry usually get confused at beginning with bunch of formula, angle values and Identities.

     But if Once, They are all learnt properly then Trigonometry becomes one of the most favourite topic of math for them.

 some of the initial Queries do most of us have while studying Trigonometry i.e.

Trigonometry Table

  •   Why Trigonometry ?  •   What are the basics of Trigonometry?  •   What are the values of Angles of various T-ratios ?

    so, For the answer of all these questions click this post:

     

  •     Trigonometry functions & Basic concepts with formula

now as I've titled this post, I'm going to reveal the best method which I recommend to construct Trigonometry table within or less than​ 5 minutes.

 •   How to construct Trigonometry table within or less than 5 minutes without memorising :

       There are 6 T-ratios and we all are well known with , and

yes, of course...!!! 

       This T-ratios posses some numerical values at different angles like 0°, 30°, 45°, 60°, 90° etc. but this doesn't mean that they don't have other values, Na !!

  Each T-ratios have numerical values for every angle from 0° to infinity but the most and commonly used angles are 0°, 30°, 45°, 60°, 90° and also 180° too and we can construct a table for such values.

so, let's start,

 •  we'll start with Sin∅ 

                  0°       30°       45°        60°    90°

sin∅         0        1/2       1/√2      √3/2     1

these values of Sin∅ at different angles we have to keep these in mind now all other values can be derived from these, how ?

look at below,

 •  for Cos∅, values will be reversed means Sin 90° = Cos 0° so,

Cos∅      1         √3/2       1/√2       1/2      0

 •  Sec∅ = 1/ Cos∅, hence Cos∅ values will reciprocate for Sec∅ :

Sec ∅     1        2/√3         √2         2        1/0 =∞

 •  Cosec∅ = 1/ Sin∅, hence Sin∅ values will reciprocate for Cosec∅ :

Cosec∅   1/0=∞     2         √2        2/√3       1

 •  Now for Tan∅ = Sin∅/Cos∅ 

Tan∅      0         1/√3       1          √3              ∞

•  And for Cot∅, values of tan∅ will get reversed  i.e.  (tan 0° = Cot 90°)

Cot∅       ∞         √3           1        1/√3          0

so, This is how we can construct the whole table within or less than 5 minutes.

look at the whole table below,

                  0°       30°       45°        60°    90°

sin∅         0        1/2       1/√2      √3/2     1

Cos∅        1       √3/2       1/√2       1/2      0

Sec ∅       1        2/√3         √2         2       ∞ 
Cosec∅   ∞         2             √2        2/√3    1

Tan∅      0         1/√3       1          √3        ∞

Cot∅       ∞         √3           1        1/√3      0

   For, finding further values there may apply certain rules which I'll discuss in my next tutorials.

Till then if you are having anything you think that should be shared here, please do let me know via comment or email. It would be pleasure for me.