1. What are Trigonometric Functions?

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

2. How Does the Calculator Work?

The calculator uses PHP's built-in trigonometric functions:

Where:

• \( \theta \) — Angle in degrees (0-360)
• sin(θ) — Sine function result (unitless)
• cos(θ) — Cosine function result (unitless)
• tan(θ) — Tangent function result (unitless)

Explanation: The calculator converts degrees to radians and calculates the three primary trigonometric functions.

3. Importance of Trigonometric Calculations

Details: Trigonometric functions are essential for solving problems involving triangles, waves, oscillations, rotations, and many real-world applications in science and engineering.

4. Using the Calculator

Tips: Enter an angle in degrees (0-360). The calculator will compute sine, cosine, and tangent values. Results are unitless ratios.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid angles?
A: The calculator accepts angles from 0 to 360 degrees, covering all possible angles in a circle.

Q2: Why are the results unitless?
A: Trigonometric functions return ratios of side lengths, which are dimensionless quantities.

Q3: What happens at 90 degrees for tangent?
A: At 90 degrees, tangent approaches infinity (undefined). The calculator will show a very large number or may show an error for exact 90 degrees.

Q4: Can I use radians instead of degrees?
A: This calculator specifically uses degrees. For radian calculations, you would need to convert manually (radians = degrees × π/180).

Q5: Are there other trigonometric functions?
A: Yes, there are also cosecant, secant, and cotangent functions, which are reciprocals of sine, cosine, and tangent respectively.