Unit circle

A unit circle is a circle whose radius is equal to 1. Furthermore, the circle has its center at the origin of a rectangular coordinate system.

Unit circle

Let P = (x , y) be a point on the circle. Then, make a right triangle by drawing a line perpendicular to x. The line is shown in green.

The horizontal leg of the triangle is x units away from the origin and the vertical leg of the triangle is y units away from the origin.



Using the pythagorean theorem, we get x2 + y2 = 12    or    x2 + y2 = 1


We can take a step further. Let us name t the angle made with the radius in red and the x axis.

Take a close look at the triangle and you will see as we learned before that the adjacent side to angle t is x and the opposite side is y.

Therefore, sin(t) = y / 1 = y   and cos(t) = x / 1 = x

We can replace x = cos(t) and sin(t) in x2 + y2 = 1

We get cos(t)2 + sin(t)2 = 1

We just derived one of the most important trigonometric identities. We have just scratched the surface of what we can do with the unit circle. Next lesson will show that the unit circle can also be used to find sin (45 degrees)





Recent Articles

  1. Linear Parent Function

    Nov 20, 17 11:18 AM

    What is a linear parent function? Crystal clear explanation.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. Linear Parent Function

    Nov 20, 17 11:18 AM

    What is a linear parent function? Crystal clear explanation.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz