Hello, premedtim!

You're expected to know the trig values for 30°, 45°, and 60°.

I'll add diagrams to what Captain Black said.

For the 45° angle, we have "half a square". Code:

+ - - - - - *
: * *
: x * *
: * * 1
: * *
: * 45° *
* * * * * * *
1

If the sides of the square are of length 1,

. . we use Pythagorus to find the length of the diagonal.

Hence:.

For a 45° angle, the sides of the right triangle are: .

If you memorize that, you can write all the trig values for 45°.

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

For the 30° and 60° angles, we have an equilateral triangle.

Draw an altitude, bisecting the vertex angle and the base. Code:

*
*:*
* : *
* : *
1 *30*: *
* : *
* : _ *
* :½√3 *
* : *
* 60* : *
* * * * * * * * * * *
½

We have a 30-60 right triangle with

Pythagorus says that:

The sides are: .

Multiply by 2: .

. . . . . . . . . opp 30° . opp 60° .hyp

If you memorize that, you can recreate these triangles any time. Code:

*
2 * *
* * 1
* 30° *
* * * * * * * * *
√3
*
**
* *
2 * * _
* *√3
* *
* *
* 60° *
* * * * *
1