1. What is the Tangent Function?

The tangent function is a fundamental trigonometric function that relates the ratio of the opposite side to the adjacent side in a right-angled triangle. It's widely used in mathematics, physics, engineering, and various scientific applications.

2. How Does the Calculator Work?

The calculator uses the tangent formula:

Where:

• \( \theta \) — Angle in the right triangle
• Opposite — Side opposite to angle θ
• Adjacent — Side adjacent to angle θ

Explanation: The tangent function calculates the ratio between the length of the side opposite to an angle and the length of the side adjacent to that angle in a right triangle.

3. Importance of Tangent Calculation

Details: Tangent calculations are essential for solving problems involving right triangles, determining angles and distances in navigation, construction, physics problems involving forces and motion, and in computer graphics for calculating perspectives and angles.

4. Using the Calculator

Tips: Enter the length of the opposite side and adjacent side in meters. Both values must be positive numbers greater than zero. The calculator will compute the tangent of the angle.

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 with a period of π radians (180 degrees).

Q2: When is the tangent function undefined?
A: The tangent function is undefined when the adjacent side equals zero, which occurs at angles of 90° and 270° (or π/2 and 3π/2 radians).

Q3: How can I find the angle from the tangent value?
A: You can use the inverse tangent function (arctan or tan⁻¹) to find the angle from a tangent value.

Q4: What are some practical applications of tangent?
A: Tangent is used in surveying to calculate heights of objects, in navigation to determine courses, in construction for calculating slopes and angles, and in physics for resolving forces.

Q5: How does tangent relate to other trigonometric functions?
A: Tangent is related to sine and cosine through the identity: tan(θ) = sin(θ)/cos(θ). It's also the reciprocal of the cotangent function.