Trigonometry Calculator
Compute sin, cos, tan, csc, sec, cot for any angle in degrees or radians. Interactive unit-circle visualization.
Math
Trigonometry Calculator
Generated on April 25, 2026
Unit Circle
45.0°Unit-circle interpretation: For an angle θ measured counter-clockwise from the +x axis, cos(θ) is the x-coordinate of the point on the unit circle, and sin(θ) is the y-coordinate. tan(θ) = sin/cos = the slope of the line from the origin to that point.
Reciprocals: csc = 1/sin, sec = 1/cos, cot = 1/tan. These are undefined when the denominator is zero (e.g., tan(90°) and sec(90°) are undefined).
?What is the Trigonometry Calculator?
The Trigonometry Calculator computes all six trigonometric ratios — sin, cos, tan and their reciprocals csc, sec, cot — for any angle in degrees or radians. Includes an interactive unit-circle visualization showing the angle's terminal point and the colored sin (vertical) and cos (horizontal) line segments, making the geometric meaning obvious instead of just abstract numbers. Quick-pick buttons for common angles (0°, 30°, 45°, 60°, 90°, 180°, 270°). Useful for trigonometry homework, physics problems, signal processing, and intuition-building about how sin and cos relate to circular motion.
The Formula
Trigonometric ratios were originally defined for right triangles (sin = opposite/hypotenuse), but the unit-circle definition extends them to ALL angles, including negative and over 360°. tan(θ) is undefined at 90° and 270° (where cos=0); csc is undefined at 0° and 180° (where sin=0); cot is undefined at 0° and 180°; sec is undefined at 90° and 270°. The values repeat every 360° (or 2π radians) — sin and cos are the most fundamental periodic functions in mathematics and physics.
Practical Examples
sin(30°) = 0.5 exactly. cos(60°) = 0.5 exactly. These are the famous 30-60-90 triangle ratios.
sin(45°) = cos(45°) = √2/2 ≈ 0.707. tan(45°) = 1 exactly.
sin(0°) = 0, cos(0°) = 1, tan(0°) = 0.
sin(90°) = 1, cos(90°) = 0, tan(90°) is undefined.
Pythagorean identity: sin²(θ) + cos²(θ) = 1 for any θ — the equation of the unit circle.
In Karachi at noon (sun ~30° above horizon in winter), a 1m vertical pole casts a shadow of length 1/tan(30°) ≈ 1.73m.
Frequently Asked Questions
Popular Conversions
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