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.
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.
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 x^{2} + y^{2} = 1We 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).
May 21, 18 09:24 AM
Explore exponential and logarithmic functions with these easy to follow math lessons
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
May 21, 18 09:24 AM
Explore exponential and logarithmic functions with these easy to follow math lessons
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
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.