Unit Circle Calculator: Exact Sin, Cos & Tan Values

Enter details

Log in or create a free account to save your inputs and results, so you don't have to enter them again next time.🔒 No spam, ever. We never sell or share your details, and you can delete your history or account at any time. Privacy policy

Fill in the details and click Calculate to see your results.

Formula at a glance

Unit Circle Calculator: Point on the circle — (x, y) = (cos θ, sin θ). Example: θ = 150° → Point on the unit circle (cos θ, sin θ): (−√3/2 ≈ −0.8660254, 1/2 ≈ 0.5) — How the Unit Circle Calculator works: Point on the circle — (x, y) = (cos θ, sin θ)

Rate this calculator

Was it useful? A quick star rating helps others — and you can leave a comment too.

Rate it: ★ ★ ★ ★ ★

📘 About the Unit Circle Calculator

The unit circle has radius 1 and its centre at the origin. The point at angle θ (measured anticlockwise from the positive x-axis) is (cos θ, sin θ), which is how sine and cosine are defined for every angle, not just those in right triangles. Special angles like 30°, 45° and 60° have exact values with square roots.

Type an angle in degrees or radians (pi/4, 5pi/6). The calculator gives the coordinates and all six trig functions — exact where possible — the quadrant and signs, the reference angle, the radian or degree equivalent, coterminal angles and a table of the special angles.

🧮 Formula

Point on the circle

(x, y) = (cos θ, sin θ)

Tangent

tan θ = sin θ / cos θ

Radians

θ(rad) = θ(°) × π/180

✏️ Worked examples

θ = 150°

You enter
Angle θ	150
Measured in	Degrees

You get
Point on the unit circle (cos θ, sin θ)	(−√3/2 ≈ −0.8660254, 1/2 ≈ 0.5)
sin θ	1/2 ≈ 0.5
cos θ	−√3/2 ≈ −0.8660254
tan θ	−√3/3 ≈ −0.57735027
csc θ · sec θ · cot θ	2 · −2√3/3 ≈ −1.1547005 · −√3 ≈ −1.7320508
Angle	150° = 5π/6 ≈ 2.6179939 rad
Quadrant	Quadrant II (sin positive)
Reference angle	30°
Coterminal angles	150°, −210°, 510°

Point (−√3/2 ≈ −0.8660254, 1/2 ≈ 0.5).

θ = π/4

You enter
Angle θ	pi/4
Measured in	Radians (pi/6 …)

You get
Point on the unit circle (cos θ, sin θ)	(√2/2 ≈ 0.70710678, √2/2 ≈ 0.70710678)
sin θ	√2/2 ≈ 0.70710678
cos θ	√2/2 ≈ 0.70710678
tan θ	1
csc θ · sec θ · cot θ	√2 ≈ 1.4142136 · √2 ≈ 1.4142136 · 1
Angle	45° = π/4 ≈ 0.78539816 rad
Quadrant	Quadrant I (all positive)
Reference angle	45°
Coterminal angles	45°, −315°, 405°

Point (√2/2 ≈ 0.70710678, √2/2 ≈ 0.70710678).

🧭 How to use this calculator

What you enter

Angle θ
Measured in

What you get

Point on the unit circle (cos θ, sin θ)
sin θ
cos θ
tan θ
csc θ · sec θ · cot θ
Angle
Quadrant
Reference angle
Coterminal angles

❓ Frequently asked questions

What is sin 60° exactly?

√3/2 ≈ 0.866. cos 60° = 1/2 and tan 60° = √3.

How do I remember the signs?

ASTC — All positive in quadrant I, Sin in II, Tan in III, Cos in IV.

What is a reference angle?

The acute angle between the terminal side and the x-axis. Trig values of θ equal those of its reference angle, up to sign.

⭕ Unit Circle Calculator: Exact sin, cos, tan Values