Sine Cosine Tangent Calculator
Calculate all trigonometric functions from angles or right triangle measurements
Calculate Trigonometric Functions
Enter any angle to calculate all trigonometric functions
Trigonometric Functions
Calculation Details
Input Angle: 0°
Angle in Radians: 0.000000 rad
Fundamental Identity: sin²(θ) + cos²(θ) = 1.000000 ≈ 1
Tangent Formula: tan(θ) = sin(θ)/cos(θ) = 0.000000/1.000000
Common Trigonometric Values
| Angle (°) | Angle (rad) | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | ∞ |
| 120° | 2π/3 | √3/2 | -1/2 | -√3 |
| 135° | 3π/4 | √2/2 | -√2/2 | -1 |
| 150° | 5π/6 | 1/2 | -√3/2 | -√3/3 |
| 180° | π | 0 | -1 | 0 |
Primary Functions
Sine (sin)
opposite / hypotenuse
Cosine (cos)
adjacent / hypotenuse
Tangent (tan)
opposite / adjacent = sin/cos
Reciprocal Functions
Key Identities
sin²(θ) + cos²(θ) = 1
tan(θ) = sin(θ)/cos(θ)
sin(90° - θ) = cos(θ)
Calculator Tips
Use angle mode for direct trigonometric calculations
Triangle mode solves right triangles from known measurements
Results include all six trigonometric functions
Common values are provided for reference
Understanding Trigonometric Functions
What are Trigonometric Functions?
Trigonometric functions are mathematical functions that relate angles to ratios of sides in right triangles. The three primary functions are sine (sin), cosine (cos), and tangent (tan), each representing specific ratios between triangle sides.
Unit Circle Definition
On the unit circle (radius = 1), these functions represent coordinates and slopes. Sine gives the y-coordinate, cosine gives the x-coordinate, and tangent represents the slope of the line from origin to the point.
Triangle Ratios
sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent
Key Properties
- • Sine and cosine values range from -1 to 1
- • Tangent can take any real value
- • Functions are periodic (repeat their values)
- • sin²(θ) + cos²(θ) = 1 for any angle θ
Applications
Engineering
Structural analysis, wave mechanics, signal processing, and mechanical design
Physics
Oscillatory motion, wave properties, circular motion, and force analysis
Navigation
GPS calculations, surveying, astronomy, and geographic positioning
Problem Solving Methods
From Angle
- 1. Input the angle in degrees or radians
- 2. Apply trigonometric functions directly
- 3. Get all primary and reciprocal functions
- 4. Verify using fundamental identities
From Triangle
- 1. Identify known sides and angles
- 2. Apply triangle solving techniques
- 3. Calculate trigonometric ratios
- 4. Verify triangle validity and ratios