1. What is the Tangent Equation?

The tangent function is a fundamental trigonometric function that relates an angle in a right triangle to the ratio of the opposite side to the adjacent side. It's one of the three primary trigonometric functions along with sine and cosine.

2. How Does the Calculator Work?

The calculator uses the tangent equation:

Where:

• \( \theta \) — Angle in degrees
• opposite — Length of the side opposite to the angle
• adjacent — Length of the side adjacent to the angle

Explanation: The calculator provides two results - the tangent value calculated from the angle using PHP's tan() function, and the ratio calculated from the opposite and adjacent sides.

3. Applications of Tangent

Details: The tangent function is widely used in mathematics, physics, engineering, and computer graphics. It's essential for solving problems involving right triangles, calculating slopes, determining angles of elevation and depression, and in various wave and oscillation calculations.

4. Using the Calculator

Tips: Enter the angle in degrees and the lengths of the opposite and adjacent sides in meters. All values must be positive numbers, with the adjacent side greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of the tangent function?
A: The tangent function can take any real value, from negative infinity to positive infinity.

Q2: When is tangent undefined?
A: Tangent is undefined at 90° and 270° (and their periodic equivalents) because the adjacent side would be zero, causing division by zero.

Q3: What's the relationship between tangent and other trig functions?
A: Tangent can be expressed as the ratio of sine to cosine: tan(θ) = sin(θ)/cos(θ).

Q4: How is tangent used in real-world applications?
A: Tangent is used in surveying to calculate heights of objects, in navigation for course plotting, in construction for determining slopes, and in physics for analyzing forces.

Q5: What are the common values of tangent?
A: Common values include tan(0°) = 0, tan(30°) = √3/3 ≈ 0.577, tan(45°) = 1, tan(60°) = √3 ≈ 1.732.