Thread: trig ratios

is it required to memorize trig ratios such as sin pi/3 = sqrt3 / 2?
will such ratios be given in examinations?

I'd doubt any exams will require you to memorise these ratios, what I can say is just make sure you are able to re-produce them in exam conditions rather than memorising them individually

are you sure of this, and what exactly is 'reproduce them' supposed to mean? i can get up to a certain point but one has to know the exact value where calculator results are not appropriate.

Hello, furor celtica!

The bad news: Yes, we're expected to know these values.

The good news: They're not that hard to learn.



For 45°, draw a square (side 1), draw a diagonal.

Code:

      * - - - - - - *
      |           * |
      |     _   *   |
      |    √2 *     | 1
      |     *       |
      |   *         |
      | * 45°       |
      * - - - - - - *
             1

Using Pythagorus, the diagonal is

And we have: .




For 30° and 60°, draw an equilateral triangle (side 2) and an alitutude.

Code:

              *
             /|\
            / | \
           /  |  \
        2 /30°| _ \ 2
         /    |√3  \
        /     |     \
       / 60°  |      \
      * - - - * - - - *
          1       1

Using Pythagorus, the altitude is


Then: . . . .

A trick which i used to remember ratios in my earlier classes(when i was new to trigonometry..)

For sine ratio

First, write 0 30 45 60 90 which are the basic ratios.

Write from 0 to 4 under each degree

Code:

0  30   45   60  90

0   1    2    3   4

Divide each by 4

Code:

0  30   45   60  90

0   1    2    3   4    
-- --   --   --  --
4   4    4    4   4

Take the square roots for each..

Code:

0  30   45   60  90

0   1    2    3   4    
-- --   --   --  --
4   4    4    4   4 

0   1    1   




   1
    --   --   --  --
    2   




    2   1

We have the sine ratio.. For co-sine ratio take sin 90 as cos 0 and you are done..