1. ## trig ratios

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

2. 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

3. 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.

4. 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 $\sqrt{2}.$

And we have: . $\begin{Bmatrix}\sin45^o &=& \dfrac{opp}{hyp} &=& \dfrac{1}{\sqrt{2}} \\ \\[-4mm]
\cos45^o &=& \dfrac{adj}{hyp} &=& \dfrac{1}{\sqrt{2}} \\ \\[-4mm]
\tan45^o &=& \dfrac{opp}{adj} &=& 1 \end{Bmatrix}$

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 $\sqrt{3}.$

Then: . $\begin{Bmatrix}\sin30^o &=& \dfrac{opp}{hyp} &=& \dfrac{1}{2} \\ \\[-4mm] \cos30^o &=& \dfrac{adj}{hyp} &=& \dfrac{\sqrt{3}}{2} \\ \\[-4mm] \tan30^o &=& \dfrac{opp}{adj} &=& \dfrac{1}{\sqrt{3}} \end{Bmatrix}$ . . . $\begin{Bmatrix}\sin60^o &=& \dfrac{opp}{hyp} &=& \dfrac{\sqrt{3}}{2} \\ \\[-4mm] \cos60^o &=& \dfrac{adj}{hyp} &=& \dfrac{1}{2} \\ \\[-4mm] \tan60^o &=& \dfrac{opp}{adj} &=& \sqrt{3} \end{Bmatrix}$

5. 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

img.top {vertical-align:15%;}

$\sqrt3$   1
--   --   --  --
2

img.top {vertical-align:15%;}

$\sqrt2$    2   1
We have the sine ratio.. For co-sine ratio take sin 90 as cos 0 and you are done..