Unit circle

It’s a fairly fundamental tool for solving trigonometric problems.

Refer to CalcWorkshop.

“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 is Cosine-Axis, and Y-axis is Sine-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 THREE images on the unit circle, so in total it's FOUR of them. Two are POSITIVE, other two are NEGATIVE.