Trigonometry Calculator
Trigonometry - Solve mathematical problems with step-by-step solutions.
Trigonometry Calculator
Angles, Sides & Functions
Enter any two values
Trigonometry
Trigonometry studies relationships between side lengths and angles of triangles. The Law of Sines and Law of Cosines can be used to solve for unknown sides and angles in any triangle, not just right-angled ones.
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.
Frequently Asked Questions
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