Unit Circle Reference
Interactive unit circle showing sin, cos, tan values for common angles in degrees and radians.
Common Angles
| ° | rad | sin | cos | tan |
|---|
About this reference
The unit circle is a circle of radius 1 centred on the origin. For any angle, the x-coordinate of the point on the circle is the cosine and the y-coordinate is the sine. This page gives the values of sine, cosine and tangent for every common angle in both degrees and radians.
Learning the table, or at least the pattern of 1/2, √2/2 and √3/2, saves time in trigonometry, calculus and physics.
How to use it
- Find your angle in degrees or radians.
- Read across for sin, cos and tan.
- Use the symmetry across quadrants to extend to other angles.
How to remember it
For 30°, 45° and 60°, sine takes the values 1/2, √2/2, √3/2 and cosine takes them in reverse. Tangent is sin ÷ cos. Signs follow the quadrant: all positive in the first, sine positive in the second, tangent positive in the third and cosine positive in the fourth. Radians = degrees × π/180.
Worked example
Key values
| 30° (π/6) | sin 1/2, cos √3/2, tan 1/√3 |
| 45° (π/4) | sin √2/2, cos √2/2, tan 1 |
| 60° (π/3) | sin √3/2, cos 1/2, tan √3 |
| 90° (π/2) | sin 1, cos 0, tan undefined |
Tips and common mistakes
- Memorise the first quadrant and use symmetry for the rest.
- Tangent is undefined where cosine is zero (90° and 270°).
- sin² + cos² = 1 at every angle.
- Convert degrees to radians by multiplying by π/180.
- Use exact surds such as √3/2 in exams and decimals for calculations.
Frequently asked questions
What is the unit circle?
A circle with radius 1 centred at the origin.
What is sin 30°?
1/2.
What is cos 60°?
1/2.
Why is tan 90° undefined?
Because cos 90° is 0, and division by zero is not defined.
How many radians in 180°?
π.
What is the value of sin² + cos²?
1.