Unit circle
It’s a fairly fundamental tool for solving
trigonometric problems
.
“Unit Circle is nothing more than a circle with a bunch of Special Right Triangles.”
Well, these special right triangles help us in connecting everything we’ve learned so far about Reference Angles, Reference Triangles, and Trigonometric Functions, and puts them all together in one nice happy circle and allow us to find angles and lengths quickly.
Special right triangles
30-60-90 Triangle
:
45-45-90 Triangle
:
Unit Circle with Special Right Triangles
:
The Complete Unit Circle
X-axis
in the image isCosine-Axis
, andY-axis
isSine-Axis
.
Exact values of the unit circle
How to memorise the Unit Circle
Refer to this PDF: unit-circle-radian-measure.pdf
Actually, we only need to remember the First Quadrant, and just REFLECT it about Y-axis and X-axis and the Origin, then we get all four quadrants of these special values.
Something important to remember:
- Each point on the
unit circle
, has other THREEimages
on the unit circle, so in total it's FOUR of them. Two are POSITIVE, other two are NEGATIVE.