1. What is Trigonometric Ratio (Tan)?

The tangent (tan) is a fundamental trigonometric ratio that relates the opposite side to the adjacent side in a right triangle. It's defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

2. How Does the Calculator Work?

The calculator uses the tangent formula:

Where:

• Opposite — Length of the side opposite to the angle θ (meters)
• Adjacent — Length of the side adjacent to the angle θ (meters)

Explanation: The calculator computes the tangent of angle θ by dividing the opposite side length by the adjacent side length.

3. Importance of Trigonometric Ratios

Details: Trigonometric ratios like tangent are essential in mathematics, physics, engineering, and navigation. They help solve problems involving right triangles and are fundamental to understanding periodic phenomena and wave functions.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of tangent values?
A: Tangent values range from negative infinity to positive infinity, as the function is periodic and undefined at 90° and 270°.

Q2: How is tangent used in real-world applications?
A: Tangent is used in surveying, construction, navigation, and physics to calculate heights, distances, and angles.

Q3: What's the relationship between tangent and other trigonometric functions?
A: Tangent is related to sine and cosine as tan(θ) = sin(θ)/cos(θ). It's also the reciprocal of cotangent.

Q4: Can tangent values be greater than 1?
A: Yes, tangent values can be greater than 1. For angles between 45° and 90°, tangent values exceed 1 and approach infinity as the angle approaches 90°.

Q5: How accurate is this calculator?
A: The calculator provides results with 4 decimal places precision, which is sufficient for most practical applications involving trigonometric calculations.