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Math

Trigonometry Calculator

Instant sin, cos, tan, sec, csc & cot — degrees or radians

Equivalent:45°0.7853981634 rad

Common Angles

Trig Functions

sin
Sinesin(θ) = opposite / hypotenuse
0.7071067812
cos
Cosinecos(θ) = adjacent / hypotenuse
0.7071067812
tan
Tangenttan(θ) = opposite / adjacent = sin/cos
1
csc
Cosecantcsc(θ) = 1 / sin(θ)
1.414213562
sec
Secantsec(θ) = 1 / cos(θ)
1.414213562
cot
Cotangentcot(θ) = cos(θ) / sin(θ)
1

Unit Circle Reference

Angle (°)Radsincostan
0°0010
30°π/61/2√3/21/√3
45°π/4√2/2√2/21
60°π/3√3/21/2√3
90°π/210
180°π0−10
270°3π/2−10
360°010

Key Identities

  • sin²(θ) + cos²(θ) = 1
  • tan(θ) = sin(θ) / cos(θ)
  • csc(θ) = 1 / sin(θ)
  • sec(θ) = 1 / cos(θ)
  • cot(θ) = cos(θ) / sin(θ)
  • 1 + tan²(θ) = sec²(θ)
  • 1 + cot²(θ) = csc²(θ)
About

Use this free trigonometry calculator to instantly find all six trig functions — sin, cos, tan, csc, sec, and cot — for any angle in degrees or radians. Whether you're working through homework, checking unit circle values, or verifying identities, this tool delivers precise results with a built-in reference table and common-angle presets for 0°, 30°, 45°, 60°, 90°, and beyond.

FAQ
How do I convert degrees to radians for trig calculations?+

Multiply degrees by π/180. For example, 45° × (π/180) = π/4 ≈ 0.7854 radians. This calculator handles the conversion automatically — just select your unit and enter the angle.

Why is tan(90°) undefined?+

tan(θ) = sin(θ)/cos(θ). At 90°, cos(90°) = 0, which means division by zero. The tangent function has vertical asymptotes at 90°, 270°, and any odd multiple of π/2 radians.

What is the difference between sin and csc?+

Cosecant (csc) is the reciprocal of sine: csc(θ) = 1/sin(θ). Similarly, sec = 1/cos and cot = 1/tan. These reciprocal functions are undefined whenever their denominator (the primary function) equals zero.

Which angles should I memorize for the unit circle?+

The key angles are 0°, 30°, 45°, 60°, and 90° (and their equivalents in other quadrants). These correspond to sine and cosine values of 0, 1/2, √2/2, √3/2, and 1 — the foundation of most trig problems.

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