Unit Circle Calculator
Each angle meets the unit circle at (cos θ, sin θ): 150° lands at (−√3/2, 1/2).
(−√3/2, 1/2)
- sin θ
- 1/2 ≈ 0.5
- cos θ
- −√3/2 ≈ -0.8660254
- tan θ
- −√3/3 ≈ -0.57735027
- Angle in radians
- 2.617993878
- Angle in degrees
- 150
- Reference angle
- 30 °
- Position
- Quadrant II
Step-by-step solution
- Reference angle = 30° (Quadrant II)
- Signs: sine positive in quadrants I–II, cosine in I and IV, tangent in I and III
- Exact values for 30°: sin 1/2, cos √3/2, tan √3/3
Unit Circle Formula
(cos θ, sin θ) on x² + y² = 1
tan θ = sin θ / cos θ; signs follow the quadrant (ASTC)
Worked Example
The angle 150°:
- Reference angle = 30° (Quadrant II)
- Signs: sine positive in quadrants I–II, cosine in I and IV, tangent in I and III
- Exact values for 30°: sin 1/2, cos √3/2, tan √3/3
cos θ: −√3/2 ≈ -0.8660254 · tan θ: −√3/3 ≈ -0.57735027 · Angle in radians: 2.617993878 · Angle in degrees: 150 · Reference angle: 30 ° · Position: Quadrant II
Test-day tip
The unit circle values come from the 30-60-90 and 45-45-90 triangles. Knowing 30°, 45° and 60° and the quadrant signs covers every angle on the SAT and ACT.
More Geometry and Trigonometry Calculators
-
Arc Length Calculator
s = rθ, A = ½r²θ
θ in radians; in degrees s = 2πr × θ/360
Example: A circle of radius 6 with a 120° central angle: Arc length s = 12.56637061.
-
Special Right Triangles Calculator
30-60-90: 1 : √3 : 2; 45-45-90: 1 : 1 : √2
short leg : long leg : hypotenuse; leg : leg : hypotenuse
Example: A 30-60-90 triangle with short leg 5: Sides: short leg = 5, long leg = 5√3, hypotenuse = 10.
-
Right Triangle Calculator
sin A = a/c, cos A = b/c, tan A = a/b
SOH-CAH-TOA; A + B = 90°
Example: A right triangle with legs 3 and 4: Hypotenuse c = 5.
-
Distance Formula Calculator
d = √[(x₂ − x₁)² + (y₂ − y₁)²]
the Pythagorean theorem on the coordinate plane
Example: The points (1, 2) and (7, 10): Distance d = 10.
Frequently asked questions
How do I remember the signs in each quadrant?
All positive in I, Sine in II, Tangent in III, Cosine in IV (“All Students Take Calculus”).
What is a reference angle?
The acute angle to the x-axis; trig values of any angle equal those of its reference angle up to sign. 150° has reference angle 30°.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Unit Circle Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/unit-circle-calculator/
IEEE
Scientific Converters, "Unit Circle Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/unit-circle-calculator/