About the Unit Circle
The unit circle is a circle of radius 1 centered at the origin. For an angle θ measured counterclockwise from the positive x-axis, the point where the angle meets the circle has coordinates (cos θ, sin θ). That one fact is why the chart is worth memorizing: it gives the exact sine and cosine of every standard angle.
Only three numbers appear in the coordinates besides 0 and 1: 1/2, √2/2 and √3/2. The first quadrant holds the pattern, and the other three quadrants repeat it with different signs. Cosine (x) is positive on the right side of the circle, and sine (y) is positive on the top half.
A good way to learn it is to work down the sheets in order: study the filled-in chart, fill in the coordinates on the practice version where the angles are given, then try the fully blank unit circle from memory. The trig values table lists the same values in rows, with tangent (sine divided by cosine) added.
Frequently Asked Questions
What is the unit circle?
The unit circle is the circle of radius 1 centered at the origin of the coordinate plane. Each point on it has coordinates (cos θ, sin θ), where θ is the angle measured counterclockwise from the positive x-axis.
How do you convert degrees to radians?
Multiply the degrees by π and divide by 180. For example, 60 degrees is 60π/180, which simplifies to π/3 radians. A full turn of 360 degrees is 2π radians.
What is the easiest way to memorize the unit circle?
Learn the first quadrant: 30, 45 and 60 degrees have coordinates built from 1/2, √2/2 and √3/2. Every other standard angle is a reflection of one of those three, so only the signs change. Then practice on a blank unit circle until you can fill it in without looking.
Why is tangent undefined at 90 and 270 degrees?
Tangent is sine divided by cosine. At 90 and 270 degrees the cosine is 0, and division by zero is undefined.
