Trigonometry Calculator
Trigonometry - Solve mathematical problems with step-by-step solutions.
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
How to use the Trigonometry Calculator
Follow these steps to get accurate results with the trigonometry calculator.
- 1
Enter your values
Fill in the required input fields above. Units can be changed where available.
- 2
Click Calculate
Press the calculate button to compute results instantly in your browser.
- 3
Review your results
View the computed outputs and use related calculators for deeper analysis.
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