Trigonometric Functions
Online calculators for trigonometric functions and angle calculations
Basic Trigonometric Functions
Sin - Sine
Calculates the sine of an angle
Cos - Cosine
Calculates the cosine of an angle
Tan - Tangent
Calculates the tangent of an angle
Cot - Cotangent
Calculates the cotangent of an angle
Sec - Secant
Calculates the secant of an angle
Csc - Cosecant
Calculates the cosecant of an angle
Inverse Trigonometric Functions (Arc Functions)
ASin - Arcsine
Inverse sine, angle from sine value
ACos - Arccosine
Inverse cosine, angle from cosine value
ATan - Arctangent
Inverse tangent, angle from tangent value
ACot - Arccotangent
Inverse cotangent, angle from cotangent value
ASec - Arcsecant
Inverse secant, angle from secant value
ACsc - Arccosecant
Inverse cosecant, angle from cosecant value
Special Functions & Conversions
ATan2 - Arctangent 2
Inverse tangent atan2(y, x) for quadrants
Sinc - Cardinal Sine
Sinc function (sin(x)/x), signal processing
Degree → Radian
Angle conversion from degrees to radians
Radian → Degree
Angle conversion from radians to degrees
About Trigonometric Functions
Trigonometric functions are fundamental mathematical functions that describe relationships between angles and side ratios in triangles. They are essential in:
- Mathematics - Geometry and calculus
- Physics - Waves and oscillations
- Engineering - Statics and mechanics
- Navigation - GPS and cartography
- Computer Graphics - 3D transformations
- Astronomy - Celestial mechanics
Function Groups
Basic Functions
sin, cos, tan - The three main functions
cot, sec, csc - Reciprocal functions
Domain: All real numbers (with exceptions)
cot, sec, csc - Reciprocal functions
Domain: All real numbers (with exceptions)
Arc Functions
arcsin, arccos, arctan - Inverse functions
arccot, arcsec, arccsc - Inverse reciprocal functions
Result: Angle in degrees or radians
arccot, arcsec, arccsc - Inverse reciprocal functions
Result: Angle in degrees or radians
Important Properties
Periodicity
• sin, cos: Period 360° (2π)
• tan, cot: Period 180° (π)
• tan, cot: Period 180° (π)
Range
• sin, cos: [-1, 1]
• tan, cot: (-∞, +∞)
• sec, csc: (-∞, -1] ∪ [1, +∞)
• tan, cot: (-∞, +∞)
• sec, csc: (-∞, -1] ∪ [1, +∞)
Identities
• sin²(α) + cos²(α) = 1
• tan(α) = sin(α)/cos(α)
• 1 + tan²(α) = sec²(α)
• tan(α) = sin(α)/cos(α)
• 1 + tan²(α) = sec²(α)
Tip: For most technical applications, radians are preferred,
as they are the natural unit for angles in calculus. The conversion between
degrees and radians is simple: 180° = π radians.
|
|
Quick Reference
Important Angles
| 0° | sin=0, cos=1 |
| 30° | sin=0.5, cos≈0.866 |
| 45° | sin≈0.707, cos≈0.707 |
| 60° | sin≈0.866, cos=0.5 |
| 90° | sin=1, cos=0 |
Conversion
Degree → Radian:
rad = (deg × π) / 180
rad = (deg × π) / 180
Radian → Degree:
deg = (rad × 180) / π
deg = (rad × 180) / π
Unit Circle
In the unit circle (radius = 1):
x = cos(α)
y = sin(α)
for any angle α
y = sin(α)
for any angle α