Trigonometric Functions Calculator
Calculate all six trigonometric functions: sin, cos, tan, sec, csc, and cot
Calculate Trigonometric Functions
Angle Information
Trigonometric Function Values
Primary Functions
Reciprocal Functions
Alternative Forms
Common Angle Examples
SOHCAHTOA Mnemonic
SOH - Sine
Sine equals Opposite over Hypotenuse
CAH - Cosine
Cosine equals Adjacent over Hypotenuse
TOA - Tangent
Tangent equals Opposite over Adjacent
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Reciprocal Trigonometric Functions
Secant (sec)
Secant is the reciprocal of cosine. It's undefined when cos(θ) = 0 (at 90°, 270°, etc.)
Cosecant (csc)
Cosecant is the reciprocal of sine. It's undefined when sin(θ) = 0 (at 0°, 180°, 360°, etc.)
Cotangent (cot)
Cotangent is the reciprocal of tangent. It's undefined when tan(θ) = 0 (at 0°, 180°, 360°, etc.)
Unit Circle Reference
Quadrant I (0° to 90°)
All functions positive
Quadrant II (90° to 180°)
Only sin and csc positive
Quadrant III (180° to 270°)
Only tan and cot positive
Quadrant IV (270° to 360°)
Only cos and sec positive
Special Angles
Quick Tips
Remember SOHCAHTOA for the basic three functions
Reciprocal functions: sec=1/cos, csc=1/sin, cot=1/tan
Use the unit circle to remember special angle values
Function signs depend on the quadrant
Pythagorean identity: sin²θ + cos²θ = 1
Understanding Trigonometric Functions
What are Trigonometric Functions?
Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. They are fundamental in mathematics, physics, engineering, and many other fields.
The Six Functions
- •Primary: sine (sin), cosine (cos), tangent (tan)
- •Reciprocal: secant (sec), cosecant (csc), cotangent (cot)
Applications
Engineering
Wave analysis, signal processing, structural analysis
Physics
Oscillations, waves, circular motion, electromagnetic fields
Computer Graphics
3D transformations, rotations, animations