1. What Are Trigonometric Functions?

Trigonometric functions (sine, cosine, tangent) are fundamental mathematical functions that relate angles of a right triangle to ratios of its sides. They have wide applications in mathematics, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator computes trigonometric values using the standard mathematical functions:

Where:

• \( x \) — Input angle value
• \( y \) — Output trigonometric value
• Angle can be in radians or degrees

Explanation: The calculator converts degrees to radians when necessary and computes the selected trigonometric function using PHP's built-in mathematical functions.

3. Importance of Trigonometric Calculations

Details: Trigonometric functions are essential for solving problems involving triangles, waves, oscillations, rotations, and periodic phenomena in various scientific and engineering applications.

4. Using the Calculator

Tips: Select the desired trigonometric function, enter the x value (angle), choose the angle unit (radians or degrees), and click calculate. The result will show the computed trigonometric value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radians and degrees?
A: Degrees divide a circle into 360 equal parts, while radians are based on the radius of the circle (2π radians = 360°).

Q2: Why does tan(x) sometimes return very large values?
A: The tangent function approaches infinity as the angle approaches odd multiples of π/2 radians (90° + n×180°).

Q3: What are the ranges of trigonometric functions?
A: Sine and cosine outputs range from -1 to 1, while tangent can be any real number.

Q4: Can I calculate inverse trigonometric functions?
A: This calculator focuses on basic trigonometric functions. Inverse functions (arcsin, arccos, arctan) would require a different implementation.

Q5: How accurate are the calculations?
A: The calculator uses PHP's built-in trigonometric functions, which provide high precision for most practical applications.