Trigonometric points !

So to know all the trignometric points in a circle,
we need help from the BIG SEVENTEEN!

<--- here it is :)

Now lets begin with the simplest points, 90° !

Since we know, all the radii are the same, x will only go as far as 1! same rules apply to y :)



So let's start with 45 ° !

1.Start by drawing out a triangle that connects the origin + point on the circumfrance of the cirlce + a vertical line that drops from the previous point.
2.Next, we can say that both angles besides the right angle which is 90° , are both 45°(180-90-45 = 45° )
3.Since both angles are equivalent, this must be an isosceles triangle ! OMG!
4.From this new information, we can say that both sides must be equal right?!
5.Also* the hypotenus must be 1, since all radii equal one in the unit circle!




Then using PYTHAGORAS THEOREM, we find X AND Y :D!!

So continue this whole first quadtrant!


PS. If you know all the points for the first quad, you know everything else as the all the points in the second quad are the same, just X becomes negative!

VOiLA! The second quad!

Here is the final product!

So if you notice, all the points have pretty much the same numbers, just rearranged differently, and are sometimes negative or positive!


Goodluck memorizing this ! :)