Trigonometry Calculator Guide
How the Trigonometry Calculator Works
Trigonometry is the study of relationships between angles and sides of triangles. The main trigonometric functions (sine, cosine, and tangent) relate the angles of a right triangle to the ratios of its sides.
The Three Main Functions
- Sine (sin): sin(θ) = opposite / hypotenuse
- Cosine (cos): cos(θ) = adjacent / hypotenuse
- Tangent (tan): tan(θ) = opposite / adjacent
Key Trigonometric Identities
Pythagorean Identity
sin²(θ) + cos²(θ) = 1
Reciprocal Identities
- csc(θ) = 1/sin(θ)
- sec(θ) = 1/cos(θ)
- cot(θ) = 1/tan(θ)
Special Angles
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° / 0 | 0 | 1 | 0 |
| 30° / π/6 | 1/2 | √3/2 | 1/√3 |
| 45° / π/4 | √2/2 | √2/2 | 1 |
| 60° / π/3 | √3/2 | 1/2 | √3 |
| 90° / π/2 | 1 | 0 | undefined |
Real-World Applications
Navigation & GPS
Trigonometry is used to calculate distances and directions, essential for GPS systems and navigation.
Architecture & Engineering
Used to calculate angles, heights, and structural loads in building design and construction.