The Unit Circle Calculator is an online mathematical tool that evaluates trigonometric values by mapping angles onto a circle with a radius of exactly one unit. By entering an angle (in degrees or radians), the calculator returns precise trigonometric values along with their coordinate representation.
This tool is especially powerful for visual learning, exam preparation, and advanced trigonometry applications.
Unit Circle in Trigonometry
The unit circle is a circle centered at the origin (0,0) with a radius of 1 unit. Every point on the circle corresponds to an angle θ, and its coordinates represent trigonometric values:
x-coordinate = cos(θ)
y-coordinate = sin(θ)
The unit circle forms the foundation of:
Trigonometric identities
Radian measure
Periodic functions
Advanced calculus concepts
Core Unit Circle Relationships (Highlighted):
cos(θ) = x
sin(θ) = y
tan(θ) = sin(θ) / cos(θ)
Unit Circle Equation:
x² + y² = 1
Where:
θ
= angle
x
= cosine value
y
= sine valueProblem: Find sin, cos, and tan for θ = 60°.
Step 1: Convert to radians (if needed)
60° = π/3
Step 2: Locate the point on the unit circle
(cos 60°, sin 60°) = (1/2, √3/2)
Step 3: Compute tangent
tan 60° = (√3/2) / (1/2) = √3
Final Results:
sin(60°) = √3/2
cos(60°) = 1/2
tan(60°) = √3