Trigonometry Calculator
Instantly calculate sine, cosine, tangent, and their inverses. Switch seamlessly between degrees and radians. Perfect for students, engineers, and math enthusiasts.
Trigonometry Calculator
Instantly calculate sine, cosine, tangent, and their inverses. Switch seamlessly between degrees and radians. Perfect for students, engineers, and math enthusiasts.
Decimal Places
What is Trigonometry?
Trigonometry explores the relationships between the angles and sides of triangles. The core functions—sine, cosine, and tangent—connect angles to side ratios in right-angled triangles, forming the foundation for fields like physics, engineering, and architecture.
Basic Trigonometric Functions
In a right-angled triangle with an angle θ:
• sin(θ) = opposite / hypotenuse
• cos(θ) = adjacent / hypotenuse
• tan(θ) = opposite / adjacent = sin(θ) / cos(θ)
Reciprocal Functions
• csc(θ) = 1 / sin(θ)
• sec(θ) = 1 / cos(θ)
• cot(θ) = 1 / tan(θ) = cos(θ) / sin(θ)
Inverse Trigonometric Functions
Inverse trigonometric functions determine the angle that corresponds to a specific side ratio:
• sin⁻¹(x) returns angle whose sine is x (range: -90° to 90°)
• cos⁻¹(x) returns angle whose cosine is x (range: 0° to 180°)
• tan⁻¹(x) returns angle whose tangent is x (range: -90° to 90°)
Common Trigonometric Values
| Angle | 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 | ∞ |
Tips for Using the Calculator
- •Select Degrees or Radians mode depending on your problem.
- •For inverse functions (e.g., sin⁻¹), ensure the input value is within the valid range (e.g., -1 to 1 for sine and cosine).
- •Note that some functions are undefined at specific angles (e.g., tan(90°) is undefined).
- •Adjust precision to control the number of decimal places in results.
- •Common angles like 0°, 30°, 45°, 60°, and 90° have well-known exact values.