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

sin(45°)
0.70710678
opposite/hypotenuse
cos(45°)
0.70710678
adjacent/hypotenuse
tan(45°)
1
opposite/adjacent

Reciprocal Functions

csc(45°)
1.41421356
hypotenuse/opposite = 1/sin
sec(45°)
1.41421356
hypotenuse/adjacent = 1/cos
cot(45°)
1
adjacent/opposite = 1/tan

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

Anglesincostancscseccot
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30°0.50.8660.57721.1551.732
45°0.7070.70711.4141.4141
60°0.8660.51.7321.15520.577
90°10undefined1undefined0