Trig Function Calculator
Calculate all 6 trigonometric functions for any angle in degrees or radians
Calculate Trigonometric Functions
Enter the angle to calculate all six trigonometric functions
Primary Trigonometric Functions
Reciprocal Functions
Angle Information
Quadrant: I
Description: All positive
Angle in degrees: 45°
Angle in radians: 0.7854 rad
Right Triangle Reference
Primary Functions:
sin(α) = opposite/hypotenuse
cos(α) = adjacent/hypotenuse
tan(α) = opposite/adjacent
Reciprocal Functions:
csc(α) = 1/sin(α)
sec(α) = 1/cos(α)
cot(α) = 1/tan(α)
Function Properties
Range:
sin, cos: [-1, 1]
tan, cot: (-∞, ∞)
sec, csc: (-∞, -1] ∪ [1, ∞)
Period:
sin, cos, sec, csc: 2π
tan, cot: π
Undefined at:
tan, sec: odd multiples of π/2
cot, csc: multiples of π
Quick Tips
All functions are periodic and repeat their values
Use the unit circle to understand function behavior
Reciprocal functions are undefined when their base function equals zero
Remember: sin²(x) + cos²(x) = 1
Understanding the 6 Trigonometric Functions
Primary Functions
Sine (sin)
The sine of an angle is the ratio of the opposite side to the hypotenuse in a right triangle.
sin(α) = opposite/hypotenuse
Cosine (cos)
The cosine of an angle is the ratio of the adjacent side to the hypotenuse in a right triangle.
cos(α) = adjacent/hypotenuse
Tangent (tan)
The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle.
tan(α) = opposite/adjacent = sin(α)/cos(α)
Reciprocal Functions
Cosecant (csc)
The cosecant is the reciprocal of the sine function.
csc(α) = 1/sin(α) = hypotenuse/opposite
Secant (sec)
The secant is the reciprocal of the cosine function.
sec(α) = 1/cos(α) = hypotenuse/adjacent
Cotangent (cot)
The cotangent is the reciprocal of the tangent function.
cot(α) = 1/tan(α) = adjacent/opposite = cos(α)/sin(α)
Applications
Engineering
Used in structural analysis, wave mechanics, and signal processing for calculating forces, oscillations, and frequencies.
Navigation
Essential for GPS systems, maritime navigation, and aviation for calculating positions, bearings, and distances.
Physics
Fundamental in describing periodic motion, wave properties, circular motion, and electromagnetic phenomena.
Common Angle Values
Angle | sin | cos | tan | csc | sec | cot |
---|---|---|---|---|---|---|
0° | 0 | 1 | 0 | undefined | 1 | undefined |
30° | 0.5 | 0.866 | 0.577 | 2 | 1.155 | 1.732 |
45° | 0.707 | 0.707 | 1 | 1.414 | 1.414 | 1 |
60° | 0.866 | 0.5 | 1.732 | 1.155 | 2 | 0.577 |
90° | 1 | 0 | undefined | 1 | undefined | 0 |