Unit Circle Calculator
Sine, cosine and tangent of any angle.
Enter your values
Enter the angle you are working with.
Choose one of: Degrees, Radians.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Coordinates
- (-0.707107, 0.707107)
- sin θ
- 0.707107
- cos θ
- -0.707107
- tan θ
- -1
- Radians
- 2.356194
- Quadrant
- Q2
Quick answer
On the unit circle, a point at angle θ has coordinates (cos θ, sin θ), and tan θ is their ratio.
(x, y) = (cos θ, sin θ)
At a glance
| What it does | Sine, cosine and tangent of any angle. |
|---|---|
| Category | Math |
| Inputs needed | Angle, Unit |
| Main output | Coordinates |
| Formula | (x, y) = (cos θ, sin θ) |
| Cost | Free — no sign-up, no download |
How to use the Unit Circle Calculator
- 1Enter the angle.
- 2Choose degrees or radians.
- 3Read the trig values and quadrant.
Inputs explained
- Angle
- Enter the angle you are working with.
- Unit
- Choose one of: Degrees, Radians.
Worked example
Using the values the calculator loads with:
Inputs
- Angle135
- UnitDegrees
Results
- Coordinates(-0.707107, 0.707107)
- sin θ0.707107
- cos θ-0.707107
- tan θ-1
- Radians2.356194
- QuadrantQ2
Frequently asked questions
Why is tan undefined at 90°?
Cosine is zero there, so the ratio divides by zero.
What are the common angles?
0, 30, 45, 60 and 90 degrees have exact surd values worth memorising.
What do I need to enter into the Unit Circle Calculator?
Just 2 values: angle, unit. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Unit Circle Calculator work out the answer?
On the unit circle, a point at angle θ has coordinates (cos θ, sin θ), and tan θ is their ratio. It applies the formula (x, y) = (cos θ, sin θ) and shows the working so you can check each step by hand.
Is the Unit Circle Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.