Trigonometry Converter

Convert between angle, sin, cos, tan, cot, sec, and csc with a unit circle view and common angles table.

Input mode
Results
Angle (degrees)45.000000°
Angle (radians)0.785398
QuadrantI
sin θ
0.707107
cos θ
0.707107
tan θ
1.000000
cot θ
1.000000
sec θ
1.414214
csc θ
1.414214
x y θ cos sin
Formulas & identities

Pythagorean identity: sin²θ + cos²θ = 1

Quotient: tan θ = sin θ / cos θ    cot θ = cos θ / sin θ

Reciprocals: sec θ = 1 / cos θ    csc θ = 1 / sin θ    cot θ = 1 / tan θ

Derived: 1 + tan²θ = sec²θ    1 + cot²θ = csc²θ

Radians ↔ degrees: rad = deg × π / 180    deg = rad × 180 / π

Degrees ↔ radians converter
Common angles table
Angleradsincostancotseccsc
0°0010∞1∞
30°π/61/2√3/2√3/3√32√3/32
45°π/4√2/2√2/211√2√2
60°π/3√3/21/2√3√3/322√3/3
90°π/210∞0∞1
180°π0−10∞−1∞
270°3π/2−10∞0∞−1
360°2π010∞1∞
FAQ
What is a trigonometric function?
A trigonometric function relates an angle of a right triangle to ratios of its sides. The three primary functions are sine (opposite / hypotenuse), cosine (adjacent / hypotenuse), and tangent (opposite / adjacent). Cotangent, secant, and cosecant are the reciprocals of tangent, cosine, and sine respectively.
How do I convert between degrees and radians?
Multiply degrees by π / 180 to get radians. Multiply radians by 180 / π to get degrees. For example, 90° = 90 × π / 180 = π/2 ≈ 1.5708 rad.
Why do some conversions have two valid answers?
If you know only sin θ, the angle can lie in two different quadrants (for instance sin 30° = sin 150° = 0.5). Use the range selector to choose the quadrant you need, or provide the angle directly for an unambiguous result.
Why does tan 90° or cot 0° show ∞?
At those angles the denominator in the ratio becomes zero, so the function is undefined. The converter marks these cases as ∞ (undefined) and will not return a numeric output for them.
Can I enter a value greater than 1 for sin or cos?
No. Sine and cosine are bounded between −1 and 1 for real angles. The converter will show an error if you enter a value outside this range. Tangent and cotangent accept any real number; secant and cosecant must be ≤ −1 or ≥ 1.

Results are rounded to 6 decimals. Use the formulas above for exact values.

The Trigonometry Converter computes all six trigonometric functions (sin, cos, tan, cot, sec, csc) for a given angle, or reconstructs the angle from any known trig value. Enter a value in the input field and pick the angle unit or range: acute (0 to 90 degrees), 0 to 180 degrees, full circle (0 to 360 degrees), or radians. The tool shows the angle in both degrees and radians, the quadrant, all six function values rounded to six decimals, and a live unit circle visualization. A separate degrees to radians converter and a reference table of common angles (0, 30, 45, 60, 90, 180, 270, 360) are included. Example: enter sin = 0.5 with range 0 to 180 to get angle = 30 degrees, cos = 0.8660, tan = 0.5774, cot = 1.7321.