Trigonometry Calculator

Trigonometric Functions:

\[ \sin(\theta), \cos(\theta), \tan(\theta), \text{etc.} \]

Result:

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1. What Are Trigonometric Functions?

Trigonometric functions relate angles of a triangle to the lengths of its sides. The primary functions are sine (sin), cosine (cos), and tangent (tan), with their inverses (asin, acos, atan) providing angles from ratios.

2. How Does the Calculator Work?

The calculator computes standard trigonometric functions:

\[ \text{sin}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] \[ \text{cos}(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Note: The calculator automatically converts between degrees and radians as needed.

3. Applications of Trigonometry

Details: Used in physics, engineering, astronomy, navigation, architecture, and many other fields involving periodic phenomena or angular measurements.

4. Using the Calculator

Tips: Enter angle in degrees for standard functions (sin, cos, tan). For inverse functions (asin, acos, atan), input should be between -1 and 1 (for asin/acos).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between degrees and radians?
A: Degrees divide a circle into 360 parts, while radians use 2π. Most calculators can work with both, but this calculator uses degrees for input.

Q2: Why does tan(90°) return a very large number?
A: The tangent function approaches infinity at 90° (π/2 radians) as cosine approaches zero.

Q3: What are the valid ranges for inverse functions?
A: asin and acos accept inputs between -1 and 1. atan accepts any real number.

Q4: How precise are the calculations?
A: Results are accurate to at least 6 decimal places.

Q5: Can I calculate hyperbolic trigonometric functions?
A: This calculator focuses on circular trigonometric functions. For hyperbolic functions (sinh, cosh, tanh), a different calculator would be needed.