Tips for a unit circle

1. Unit circle A circle centered at the origin with radius 1.
It is also defined by 𝑥2
+ 𝑦2
= 1 equation that every point must
satisfy but how can we determined the position of a point in a circle
given its coordinates and equation?
Just by familiarizing this
=r on
<r in
>r out
That is what a unit circle looks like, usually people are memorizing the entire
Circle for them not to do solving anymore. BUT.THAT.IS.NOT.POSSIBLE.TO.EVERYONE.
That’s why…

2. This is the Quadrant 1 of a Unit circle, all you have to do
is to familiarize this side and you should know its
reference angle and its coterminal angle
EXAMPLE:
Pattern:
Quadrant 1 ( +,+)
Quadrant 2 ( -,+)
Quadrant 3 (-,-)
Quadrant 4 (+,-)
Sin (
3𝜋
4
)
 Covert the given into degree since its radian angle (Vice versa)
 Subtract the given into 180° to get the reference angle
 Use this equation to determine the coterminal 𝜽 + 𝟑𝟔𝟎𝒌° (K is an integer)
Reference Angle - 45° or
𝜋
4
Use the pattern that I gave since it’s 135 ̊
then is from 2nd Quadrant
So the coordinates of this given is (−
2
2
,
2
2
)
( cos, sin) (x,y)
=
2
2
3𝜋
4
*
180°
𝜋
= 135°
135°- 180° = 45°